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Absolute Value Equations — Easy Worksheet 1
Grade 9 · MathSheets Name: ____________________ Date: __________
Solve for x. There are two solutions.
How to solve
An absolute value equals k when the inside equals k or -k. Write two equations, x - h = k and x - h = -k, and solve each one. Write both solutions as x = a or x = b.
Example
|x - 5| = 6
Answer: x = 11 or x = -1
Not quite. The answer is
💡 |x| = 7 means x is 7 units from 0, so x = 7 or x = −7.
✓ Correct!
Not quite. The answer is
💡 |x| = 7 means x is 7 units from 0, so x = 7 or x = −7.
💡 How to solve: Absolute Value Equations
An absolute value equals k when the inside equals k or -k. Write two equations, x - h = k and x - h = -k, and solve each one. Write both solutions as x = a or x = b.
Try a similar one
|x + 3| = 5
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 |x| = 5 means x is 5 units from 0, so x = 5 or x = −5.
✓ Correct!
Not quite. The answer is
💡 |x| = 5 means x is 5 units from 0, so x = 5 or x = −5.
💡 How to solve: Absolute Value Equations
An absolute value equals k when the inside equals k or -k. Write two equations, x - h = k and x - h = -k, and solve each one. Write both solutions as x = a or x = b.
Try a similar one
|x - 2| = 7
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 |x − 2| = 2 means x − 2 is 2 units from 0, so x − 2 = 2 or x − 2 = −2. Add 2 to both sides: x = 2 + 2 = 4 or x = −2 + 2 = 0. So x = 4 or x = 0.
✓ Correct!
Not quite. The answer is
💡 |x − 2| = 2 means x − 2 is 2 units from 0, so x − 2 = 2 or x − 2 = −2. Add 2 to both sides: x = 2 + 2 = 4 or x = −2 + 2 = 0. So x = 4 or x = 0.
💡 How to solve: Absolute Value Equations
An absolute value equals k when the inside equals k or -k. Write two equations, x - h = k and x - h = -k, and solve each one. Write both solutions as x = a or x = b.
Try a similar one
|x + 1| = 7
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 |x + 5| = 3 means x + 5 is 3 units from 0, so x + 5 = 3 or x + 5 = −3. Subtract 5 from both sides: x = 3 − 5 = −2 or x = −3 − 5 = −8. So x = −2 or x = −8.
✓ Correct!
Not quite. The answer is
💡 |x + 5| = 3 means x + 5 is 3 units from 0, so x + 5 = 3 or x + 5 = −3. Subtract 5 from both sides: x = 3 − 5 = −2 or x = −3 − 5 = −8. So x = −2 or x = −8.
💡 How to solve: Absolute Value Equations
An absolute value equals k when the inside equals k or -k. Write two equations, x - h = k and x - h = -k, and solve each one. Write both solutions as x = a or x = b.
Try a similar one
|x - 1| = 6
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 |x − 5| = 6 means x − 5 is 6 units from 0, so x − 5 = 6 or x − 5 = −6. Add 5 to both sides: x = 6 + 5 = 11 or x = −6 + 5 = −1. So x = 11 or x = −1.
✓ Correct!
Not quite. The answer is
💡 |x − 5| = 6 means x − 5 is 6 units from 0, so x − 5 = 6 or x − 5 = −6. Add 5 to both sides: x = 6 + 5 = 11 or x = −6 + 5 = −1. So x = 11 or x = −1.
💡 How to solve: Absolute Value Equations
An absolute value equals k when the inside equals k or -k. Write two equations, x - h = k and x - h = -k, and solve each one. Write both solutions as x = a or x = b.
Try a similar one
|x| = 5
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 |x + 4| = 7 means x + 4 is 7 units from 0, so x + 4 = 7 or x + 4 = −7. Subtract 4 from both sides: x = 7 − 4 = 3 or x = −7 − 4 = −11. So x = 3 or x = −11.
✓ Correct!
Not quite. The answer is
💡 |x + 4| = 7 means x + 4 is 7 units from 0, so x + 4 = 7 or x + 4 = −7. Subtract 4 from both sides: x = 7 − 4 = 3 or x = −7 − 4 = −11. So x = 3 or x = −11.
💡 How to solve: Absolute Value Equations
An absolute value equals k when the inside equals k or -k. Write two equations, x - h = k and x - h = -k, and solve each one. Write both solutions as x = a or x = b.
Try a similar one
|x| = 1
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 |x + 2| = 5 means x + 2 is 5 units from 0, so x + 2 = 5 or x + 2 = −5. Subtract 2 from both sides: x = 5 − 2 = 3 or x = −5 − 2 = −7. So x = 3 or x = −7.
✓ Correct!
Not quite. The answer is
💡 |x + 2| = 5 means x + 2 is 5 units from 0, so x + 2 = 5 or x + 2 = −5. Subtract 2 from both sides: x = 5 − 2 = 3 or x = −5 − 2 = −7. So x = 3 or x = −7.
💡 How to solve: Absolute Value Equations
An absolute value equals k when the inside equals k or -k. Write two equations, x - h = k and x - h = -k, and solve each one. Write both solutions as x = a or x = b.
Try a similar one
|x + 3| = 3
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 |x − 1| = 4 means x − 1 is 4 units from 0, so x − 1 = 4 or x − 1 = −4. Add 1 to both sides: x = 4 + 1 = 5 or x = −4 + 1 = −3. So x = 5 or x = −3.
✓ Correct!
Not quite. The answer is
💡 |x − 1| = 4 means x − 1 is 4 units from 0, so x − 1 = 4 or x − 1 = −4. Add 1 to both sides: x = 4 + 1 = 5 or x = −4 + 1 = −3. So x = 5 or x = −3.
💡 How to solve: Absolute Value Equations
An absolute value equals k when the inside equals k or -k. Write two equations, x - h = k and x - h = -k, and solve each one. Write both solutions as x = a or x = b.
Try a similar one
|x + 1| = 5
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Absolute Value Equations — Easy Worksheet 1
Solve for x. There are two solutions.