# LINEAR EQUATIONS WORKSHEET WITH ANSWERS

Question 1 :

Solve for r :

7r + 7  =  13 + 6r

Question 2 :

Solve for x :

13 - 4x  =  1 - x

Question 3 :

Solve for x.

-7x - 3x + 2  =  -8x - 8

Question 4 :

Solve for b :

-14 + 6b + 7 - 2b  =  1 + 5b

Question 5 :

Solve for x :

-6x - 20  =  -2x + 4(1 - 3x)

Question 6 :

Solve for n :

4n - 40  =  7(-2n + 2)

Question 7 :

Solve for x :

-31 - 4x  =  -5 - 5(1 + 5x)

Question 8 :

Solve for x

-3(x - 1) + 8(x - 3)  =  6x + 7 - 5x

Question 9 :

Solve for x :

4(-8x + 5)  =  -32x - 26

Question 10 :

Solve the following equation :

(1/2)(8y - 6)  =  5y - (y + 3) Question 1 :

Solve for r :

7r + 7  =  13 + 6r

7r + 7  =  13 + 6r

Subtract 6r from each side.

r + 7  =  13

Subtract 7 from each side.

r  =  6

Question 2 :

Solve for x :

13 - 4x  =  1 - x

13 - 4x  =  1 - x

13  =  1 + 3x

Subtract 1 from each side.

12  =  3x

Divide each side by 3.

4  =  x

Question 3 :

Solve for x.

-7x - 3x + 2  =  -8x - 8

-7x - 3x + 2  =  -8x - 8

Combine the like terms.

-10x + 2  =  -8x - 8

2  =  2x - 8

10  =  2x

Divide each side by 2.

5  =  x

Question 4 :

Solve for b :

-14 + 6b + 7 - 2b  =  1 + 5b

-14 + 6b + 7 - 2b  =  1 + 5b

Combine the like terms.

4b - 7  =  1 + 5b

Subtract 4b from each side.

-7  =  1 + b

Subtract 1 from each side.

-8  =  b

Question 5 :

Solve for x :

-6x - 20  =  -2x + 4(1 - 3x)

-6x - 20  =  -2x + 4(1 - 3x)

Simplify.

-6x - 20  =  -2x + 4 - 12x

-6x - 20  =  4 - 14x

8x - 20  =  4

8x  =  24

Divide each side by 8.

x  =  3

Question 6 :

Solve for n :

4n - 40  =  7(-2n + 2)

4n - 40  =  7(-2n + 2)

Simplify.

4n - 40  =  -14n + 14

18n - 40  =  14

18n  =  54

Divide each side by 18.

n  =  3

Question 7 :

Solve for x :

-31 - 4x  =  -5 - 5(1 + 5x)

-31 - 4x  =  -5 - 5(1 + 5x)

Simplify.

-31 - 4x  =  -5 - 5 - 25x

-31 - 4x  =  -10 - 25x

-31 + 21x  =  -10

21x  =  21

Divide each side by 21.

x  =  1

Question 8 :

Solve for x

-3(x - 1) + 8(x - 3)  =  6x + 7 - 5x

-3(x - 1) + 8(x - 3)  =  6x + 7 - 5x

Simplify.

-3x + 3 + 8x - 24  =  x + 7

5x - 21  =  x + 7

Subtract x from each side.

4x - 21  =  7

4x  =  28

Divide each side by 4.

x  =  7

Question 9 :

Solve for x :

4(-8x + 5)  =  -32x - 26

4(-8x + 5)  =  -32x - 26

Simplify.

-32x + 20  =  -32x - 26

20  =  -26

In the final step of solving the given equation, the variable 'x' is no more.

And also, the result '20  =  -26' is false.

So, the given equation has no solution.

Question 10 :

Solve the following equation :

(1/2)(8y - 6)  =  5y - (y + 3)

(1/2)(8y - 6)  =  5y - (y + 3)

Simplify both sides.

4y - 3  =  5y - y - 3

4y - 3  =  4y - 3

Subtract 4y from each side.

-3  =  -3

In the final step of solving the given equation, the variable 'x' is no more.

And also, the result '-3  =  -3' is true.

Because the result is true, the given equation is true for all real values of x.

So, the given equation has infinitely has many solutions. Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

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