Question

solving multi - step equations: digital self - checking practice
exercises
2x + 3 = 4x - 5
3(x + 2)-2 = 4(x - 3)+1
6 - 3x = 5x + 7
2(3x + 4)-5 = 4(2x - 1)+3
5(2x + 3)-7 = 3(x - 2)
6x + 2 = 2x + 18

Explanation:

Step1: Solve \(2x + 3 = 4x - 5\)

Subtract \(2x\) from both sides: \(3 = 2x - 5\)
Add 5 to both sides: \(8 = 2x\)
Divide by 2: \(x = 4\)

Step2: Solve \(3(x + 2)-2 = 4(x - 3)+1\)

Expand: \(3x + 6 - 2 = 4x - 12 + 1\)
Simplify: \(3x + 4 = 4x - 11\)
Subtract \(3x\) and add 11: \(15 = x\)

Step3: Solve \(6 - 3x = 5x + 7\)

Add \(3x\) and subtract 7: \(-1 = 8x\)
Divide: \(x = -\frac{1}{8}\)

Step4: Solve \(2(3x + 4)-5 = 4(2x - 1)+3\)

Expand: \(6x + 8 - 5 = 8x - 4 + 3\)
Simplify: \(6x + 3 = 8x - 1\)
Subtract \(6x\) and add 1: \(4 = 2x\)
Divide: \(x = 2\)

Step5: Solve \(5(2x + 3)-7 = 3(x - 2)\)

Expand: \(10x + 15 - 7 = 3x - 6\)
Simplify: \(10x + 8 = 3x - 6\)
Subtract \(3x\) and 8: \(7x = -14\)
Divide: \(x = -2\)

Step6: Solve \(6x + 2 = 2x + 18\)

Subtract \(2x\) and 2: \(4x = 16\)
Divide: \(x = 4\)

Answer:

1. \(2x + 3 = 4x - 5\): \(x = 4\)
2. \(3(x + 2)-2 = 4(x - 3)+1\): \(x = 15\)
3. \(6 - 3x = 5x + 7\): \(x = -\frac{1}{8}\)
4. \(2(3x + 4)-5 = 4(2x - 1)+3\): \(x = 2\)
5. \(5(2x + 3)-7 = 3(x - 2)\): \(x = -2\)
6. \(6x + 2 = 2x + 18\): \(x = 4\)