Remember this kind of problem from primary school?
? + 5 = 7
If you like this Site about Solving Math Problems, please let Google know by clicking the +1 button. If you like this Page, please click that +1 button, too. Note: If a +1 button is dark blue, you have already +1'd it. Type your algebra problem into the text box. For example, enter 3x+2=14 into the text box to get a step-by-step explanation of how to solve 3x+2=14. Try this example now! Solving Word Problems using Algebra (Worksheets) Objective: I know how to solve word problems using algebra. Related Topics: More Lessons for Grade 8 More Lessons for Grade 9 Math Worksheets. We hope that the free math worksheets have been helpful. We encourage parents and teachers to select the topics according to the needs of the child. In this GED Math: Quantitative, Arithmetic & Algebraic Problem Solving study guide are dozens of entertaining math video lessons developed by professional educators to ensure you have a quality. Engaging math books and online learning for students ages 8-13. Pages in category 'Algebra Problems' This category contains only the following page. 2006 iTest Problems/Problem 36. Category: Math Problems; Art of Problem Solving is an ACS WASC Accredited School. AoPS Online Beast Academy AoPS Academy.
We just needed to figure out which number should go into the box to make it a true statement. Clearly, we need to replace the question mark with '2':
2 + 5 = 7
Solving equations using algebra is really no different. Instead of using a box, we use a letter to represent a number. Our task is to find the correct number (or sometimes there may be more than one number) that makes the equation true.
Sometimes we can 'see' the right answer if it is simple (maybe we can just count up with our fingers, or whatever.) But when our equations become more complicated, we need a process to follow that will eventually give us the answer.
Our Process
- We are aiming to get x (or whatever letter the question uses) on the left hand side of the equals sign, by itself.
- We solve equations by balancing: whatever we do to one side of an equation, we must do the same to the other side. So if we add 4 to the left hand side, we must add 4 to the right hand side as well. If we multiply on the left side by 2, we multiply on the right side by 2 as well.
Example 1
Solve the equation
x − 6 = 10
Answer
We need to 'get rid of' the -6 on the left hand side so we are left with x only on the left hand side.
The opposite of subtracting 6 is adding 6.
If we add 6 to both sides, we will remove the -6 on the left.
x − 6 = 10
x − 6 + 6 = 10 + 6
x = 16
So the value of x needs to be 16 to make the equation true.
CHECK into the original question:
16 − 6 = 10. It checks out okay.
Example 2
Solve 5x = 35
Answer
This time we are answering
5 × ? = 35
We could do this in our heads easily (right?), but if the problem is more complicated, we need to know what to do.
On the left, we are multiplying our unknown quantity by 5. We'll use 'x' for this quantity.
`5x = 35`
The opposite of multiplying by 5 is dividing by 5. So we divide both sides by 5:
`(5x)/5=35/5`
We obtain :
`x = 7`
CHECK: 5 × 7 = 35. It checks out okay.
[These checks seem silly with easy examples, but it is a really good idea to check your solutions for all the equation problems that you do. It means you can leave the problem feeling good that you have the right answer and also, you learn more about how the solution works.]
Example 3
Solve
`(3x)/4=7`
Answer
This time we need to do 2 steps to solve the equation. We notice there is a 4 on the bottom of the fraction.
`(3x)/4=7`
This is equivalent to dividing by 4. The opposite to dividing by 4 is multiplying by 4. So we do that first:
`(3x)/4 xx 4=7xx4`
Cancelling the 4's on the left gives:
`3x=28`
In the middle step we cancelled out the 4's, so we are left with no fraction.
Now we need to divide both sides by 3, since we have a '3×' on the left hand side of the equation.
`x=28/3=9 1/3`
Some countries (like the USA) will leave the answer as a single fraction (28/3), while the practice in other countries (like the UK and Australia) is to express the answer as a mixed numeral.
CHECK:
Is our answer correct?
Substituting our answer in the left hand side gives:
`(3x)/4=3/4 x=3/4 xx 28/3`
Canceling the 3's (which gives us 1) and the 28 with the 4 gives us 7:
`3/4 xx 28/3 = 7`
How to Program a Chevy Garage Door Opener One useful feature many new Chevrolet models come equipped with today is the Chevy Homelink garage door opener. If your vehicle is equipped with this useful feature, you might be wondering how to program it to fully enjoy its convenience. Use this procedure for New Body Style.1. Close all vehicle doors. Insert the key into the ignition. Hold down the power UNLOCK butto. The vehicle comes equipped with two transmitters. The receiver can be programmed to accept up to four transmitters. If the number of transmitters programmed. Download program chevy transmitter car kit. With the Chevrolet Shop, you can browse and install apps for things like music and audiobooks directly onto your Chevrolet MyLink. Teen Driver technology Chevrolet offers a built-in system to help encourage safe driving habits, and with its industry-first in-vehicle report card, Teen Driver can let parents know how their teenager drove the. CHEVROLET Automotive remote programming instructions. Free keyless fob procedures for your new or used replacement fob.
The right hand side in the question was 7, so we are confident our answer is correct.
Example 4
Solve 5 − (x + 2) = 5x
Answer
First, we expand out the bracket.
`5 - (x + 2) = 5x`
`5 - x - 2 = 5x`
`3 - x = 5x`
Now we recognise that it is easier to get all the x's on the right side, by adding x to both sides :
`3 = 6x`
Now I divide both sides by 6 and swap the sides:
`x = 0.5.`
CHECK:
We check our answer in both sides of the equation. If it works, it must be the right answer.
LHS = `5 - (0.5 + 2) = 2.5`
RHS = `5 xx 0.5 = 2.5` = LHS.
Checks OK.
Math Word Problem Solver Algebra
Example 5
Solve 5x − 2(x − 5) = 4x
Answer
Expanding the bracket:
`5x - 2(x - 5) = 4x`
`5x - 2x + 10 = 4x`
`3x + 10 = 4x`
Subtracting `3x` from both sides and swapping sides gives:
`x = 10`
CHECK:
LHS = `5 xx 10 - 2(10 - 5) = 50 - 10 = 40`
RHS = `4 xx 10 = 40` = LHS.
Checks OK.
Example 6
If you can, solve the equation
− (7 − x) + 5 = x + 7
What do you conclude?
Answer
− (7 − x) + 5 = x + 7
Expand out the brackets:
−7 + x + 5 = x + 7
Subtract x from both sides:
`-7+5=7`
Simplify the left hand side:
`-2 = 7` ????
Math Algebra Problem Solving
This is not possible, so we conclude that there are no possible values for x. Operationsturks and caicos virtual.
`5x = 35`
The opposite of multiplying by 5 is dividing by 5. So we divide both sides by 5:
`(5x)/5=35/5`
We obtain :
`x = 7`
CHECK: 5 × 7 = 35. It checks out okay.
[These checks seem silly with easy examples, but it is a really good idea to check your solutions for all the equation problems that you do. It means you can leave the problem feeling good that you have the right answer and also, you learn more about how the solution works.]
Example 3
Solve
`(3x)/4=7`
Answer
This time we need to do 2 steps to solve the equation. We notice there is a 4 on the bottom of the fraction.
`(3x)/4=7`
This is equivalent to dividing by 4. The opposite to dividing by 4 is multiplying by 4. So we do that first:
`(3x)/4 xx 4=7xx4`
Cancelling the 4's on the left gives:
`3x=28`
In the middle step we cancelled out the 4's, so we are left with no fraction.
Now we need to divide both sides by 3, since we have a '3×' on the left hand side of the equation.
`x=28/3=9 1/3`
Some countries (like the USA) will leave the answer as a single fraction (28/3), while the practice in other countries (like the UK and Australia) is to express the answer as a mixed numeral.
CHECK:
Is our answer correct?
Substituting our answer in the left hand side gives:
`(3x)/4=3/4 x=3/4 xx 28/3`
Canceling the 3's (which gives us 1) and the 28 with the 4 gives us 7:
`3/4 xx 28/3 = 7`
How to Program a Chevy Garage Door Opener One useful feature many new Chevrolet models come equipped with today is the Chevy Homelink garage door opener. If your vehicle is equipped with this useful feature, you might be wondering how to program it to fully enjoy its convenience. Use this procedure for New Body Style.1. Close all vehicle doors. Insert the key into the ignition. Hold down the power UNLOCK butto. The vehicle comes equipped with two transmitters. The receiver can be programmed to accept up to four transmitters. If the number of transmitters programmed. Download program chevy transmitter car kit. With the Chevrolet Shop, you can browse and install apps for things like music and audiobooks directly onto your Chevrolet MyLink. Teen Driver technology Chevrolet offers a built-in system to help encourage safe driving habits, and with its industry-first in-vehicle report card, Teen Driver can let parents know how their teenager drove the. CHEVROLET Automotive remote programming instructions. Free keyless fob procedures for your new or used replacement fob.
The right hand side in the question was 7, so we are confident our answer is correct.
Example 4
Solve 5 − (x + 2) = 5x
Answer
First, we expand out the bracket.
`5 - (x + 2) = 5x`
`5 - x - 2 = 5x`
`3 - x = 5x`
Now we recognise that it is easier to get all the x's on the right side, by adding x to both sides :
`3 = 6x`
Now I divide both sides by 6 and swap the sides:
`x = 0.5.`
CHECK:
We check our answer in both sides of the equation. If it works, it must be the right answer.
LHS = `5 - (0.5 + 2) = 2.5`
RHS = `5 xx 0.5 = 2.5` = LHS.
Checks OK.
Math Word Problem Solver Algebra
Example 5
Solve 5x − 2(x − 5) = 4x
Answer
Expanding the bracket:
`5x - 2(x - 5) = 4x`
`5x - 2x + 10 = 4x`
`3x + 10 = 4x`
Subtracting `3x` from both sides and swapping sides gives:
`x = 10`
CHECK:
LHS = `5 xx 10 - 2(10 - 5) = 50 - 10 = 40`
RHS = `4 xx 10 = 40` = LHS.
Checks OK.
Example 6
If you can, solve the equation
− (7 − x) + 5 = x + 7
What do you conclude?
Answer
− (7 − x) + 5 = x + 7
Expand out the brackets:
−7 + x + 5 = x + 7
Subtract x from both sides:
`-7+5=7`
Simplify the left hand side:
`-2 = 7` ????
Math Algebra Problem Solving
This is not possible, so we conclude that there are no possible values for x. Operationsturks and caicos virtual.
[There was a hint in the question that something funny may be going on. Always be aware that an equation may not have solutions. Also, there are times when you get solutions that cannot possibly work, so you have to discount them. We find such examples later in Equations with Radicals.]
I've always found that working example problems is the best way to understand a new subject. If you've had trouble grasping a new algebra concept, the best solution might be to work your way through a series of example problems. I've tried to compile some links for example problems you can solve.
Algebra Examples:
Intermediate Algebra Example Problems – some extra selections sorted by subject matter to illustrate each concept in more detail.
Analyze Math Algebra 1 Tutorial – A standard tutorial that focuses heavily on worked-out examples, including these problems.
