Equation Solver worksheet

1. Solution: No solution

1. Start with the equation as you typed it

   $\text{4(x - 1) + 5 = 4x + 14}$

2. Tidy up each side: multiply out any brackets, then combine terms of the same kind, such as the x terms and the plain numbers

   $\text{4x + 1 = 4x + 14}$

3. Subtract 4x from both sides. That gathers every x on the left and keeps the two sides equal

   $\text{1 = 14}$

4. Subtract 1 from both sides. That moves the plain numbers to the right

   $\text{0 = 13}$

5. The x terms cancel out. What's left, 0 = 13, is never true, so no value of x works

   $\text{No solution}$

2. Solution: No solution

1. Start with the equation as you typed it

   $\text{2(x - 3) + 6 = 2x + 14}$

2. Tidy up each side: multiply out any brackets, then combine terms of the same kind, such as the x terms and the plain numbers

   $\text{2x = 2x + 14}$

3. Subtract 2x from both sides. That gathers every x on the left and keeps the two sides equal

   $\text{0 = 14}$

4. The x terms cancel out. What's left, 0 = 14, is never true, so no value of x works

   $\text{No solution}$

3. Solution: x = 8

1. Start with the equation as you typed it

   $\text{3(x - 2) + 2 = 2x + 4}$

2. Tidy up each side: multiply out any brackets, then combine terms of the same kind, such as the x terms and the plain numbers

   $\text{3x − 4 = 2x + 4}$

3. Subtract 2x from both sides. That gathers every x on the left and keeps the two sides equal

   $\text{x − 4 = 4}$

4. Add 4 to both sides. That moves the plain numbers to the right

   $\text{x = 8}$

5. Check your answer: put x = 8 back into each side of the original equation. Both sides come out the same

   $\text{left = 20, right = 20}$

6. So the solution is

   $\text{x = 8}$

4. Solution: x = −12

1. Start with the equation as you typed it

   $\text{1(x - 2) + 1 = 2x + 11}$

2. Tidy up each side: multiply out any brackets, then combine terms of the same kind, such as the x terms and the plain numbers

   $\text{x − 1 = 2x + 11}$

3. Subtract 2x from both sides. That gathers every x on the left and keeps the two sides equal

   $\text{−x − 1 = 11}$

4. Add 1 to both sides. That moves the plain numbers to the right

   $\text{−x = 12}$

5. Divide both sides by −1, the number in front of x, so x stands alone

   $x$$=\frac{\text{12}}{\text{−1}}$$=\text{−12}$

6. Check your answer: put x = −12 back into each side of the original equation. Both sides come out the same

   $\text{left = −13, right = −13}$

7. So the solution is

   $\text{x = −12}$

5. Solution: No solution

1. Start with the equation as you typed it

   $\text{2(x - 1) + 1 = 2x + 9}$

2. Tidy up each side: multiply out any brackets, then combine terms of the same kind, such as the x terms and the plain numbers

   $\text{2x − 1 = 2x + 9}$

3. Subtract 2x from both sides. That gathers every x on the left and keeps the two sides equal

   $\text{−1 = 9}$

4. Add 1 to both sides. That moves the plain numbers to the right

   $\text{0 = 10}$

5. The x terms cancel out. What's left, 0 = 10, is never true, so no value of x works

   $\text{No solution}$

6. Solution: x = 8

1. Start with the equation as you typed it

   $\text{5(x - 2) + 2 = 3x + 8}$

2. Tidy up each side: multiply out any brackets, then combine terms of the same kind, such as the x terms and the plain numbers

   $\text{5x − 8 = 3x + 8}$

3. Subtract 3x from both sides. That gathers every x on the left and keeps the two sides equal

   $\text{2x − 8 = 8}$

4. Add 8 to both sides. That moves the plain numbers to the right

   $\text{2x = 16}$

5. Divide both sides by 2, the number in front of x, so x stands alone

   $x$$=\frac{\text{16}}{\text{2}}$$=\text{8}$

6. Check your answer: put x = 8 back into each side of the original equation. Both sides come out the same

   $\text{left = 32, right = 32}$

7. So the solution is

   $\text{x = 8}$

7. Solution: x = 10/3

1. Start with the equation as you typed it

   $\text{5(x - 1) + 6 = 2x + 11}$

2. Tidy up each side: multiply out any brackets, then combine terms of the same kind, such as the x terms and the plain numbers

   $\text{5x + 1 = 2x + 11}$

3. Subtract 2x from both sides. That gathers every x on the left and keeps the two sides equal

   $\text{3x + 1 = 11}$

4. Subtract 1 from both sides. That moves the plain numbers to the right

   $\text{3x = 10}$

5. Divide both sides by 3, the number in front of x, so x stands alone

   $x$$=\frac{\text{10}}{\text{3}}$

6. Check your answer: put x = 10/3 back into each side of the original equation. Both sides come out the same

   $\text{left = 53/3, right = 53/3}$

7. So the solution is

   $\text{x = 10/3}$

8. Solution: x = 4/5

1. Start with the equation as you typed it

   $\text{6(x - 1) + 7 = 1x + 5}$

2. Tidy up each side: multiply out any brackets, then combine terms of the same kind, such as the x terms and the plain numbers

   $\text{6x + 1 = x + 5}$

3. Subtract x from both sides. That gathers every x on the left and keeps the two sides equal

   $\text{5x + 1 = 5}$

4. Subtract 1 from both sides. That moves the plain numbers to the right

   $\text{5x = 4}$

5. Divide both sides by 5, the number in front of x, so x stands alone

   $x$$=\frac{\text{4}}{\text{5}}$

6. Check your answer: put x = 4/5 back into each side of the original equation. Both sides come out the same

   $\text{left = 29/5, right = 29/5}$

7. So the solution is

   $\text{x = 4/5}$

9. Solution: No solution

1. Start with the equation as you typed it

   $\text{3(x - 1) + 2 = 3x + 9}$

2. Tidy up each side: multiply out any brackets, then combine terms of the same kind, such as the x terms and the plain numbers

   $\text{3x − 1 = 3x + 9}$

3. Subtract 3x from both sides. That gathers every x on the left and keeps the two sides equal

   $\text{−1 = 9}$

4. Add 1 to both sides. That moves the plain numbers to the right

   $\text{0 = 10}$

5. The x terms cancel out. What's left, 0 = 10, is never true, so no value of x works

   $\text{No solution}$

10. Solution: x = −7

1. Start with the equation as you typed it

   $\text{1(x - 2) + 1 = 3x + 13}$

2. Tidy up each side: multiply out any brackets, then combine terms of the same kind, such as the x terms and the plain numbers

   $\text{x − 1 = 3x + 13}$

3. Subtract 3x from both sides. That gathers every x on the left and keeps the two sides equal

   $\text{−2x − 1 = 13}$

4. Add 1 to both sides. That moves the plain numbers to the right

   $\text{−2x = 14}$

5. Divide both sides by −2, the number in front of x, so x stands alone

   $x$$=\frac{\text{14}}{\text{−2}}$$=\text{−7}$

6. Check your answer: put x = −7 back into each side of the original equation. Both sides come out the same

   $\text{left = −8, right = −8}$

7. So the solution is

   $\text{x = −7}$