Question

onus practice!
i can distribute and combine like terms.
79.) 3(4x + 4x - x)
80.) 7(9x + 4) + 6(x - 2)
81.) -4(10 - 2x) + 12 - 3x
82.) 6(7x + 5y) - 2y + 9x
83.) -3(2x + 1)
84.) 5 - 2(x + 6)
i can solve for a variable.
for each equation below, solve for x and simplify if possible.
85.) 2x + 5 = -3
86.) (3/2)x - 4 = 11
87.) 10x + 4 = 20
88.) 6x + 2 = 2x - 1
89.) (3/4)x - 4 = 2
90.) 3x + 4 = 2x - 6

Explanation:

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

Subtract 5 from both sides: \(2x + 5 - 5 = -3 - 5\) → \(2x = -8\)
Divide by 2: \(\frac{2x}{2} = \frac{-8}{2}\) → \(x = -4\)

Step2: Solve \(\frac{3}{2}x - 4 = 11\)

Add 4: \(\frac{3}{2}x - 4 + 4 = 11 + 4\) → \(\frac{3}{2}x = 15\)
Multiply by \(\frac{2}{3}\): \(x = 15\times\frac{2}{3}\) → \(x = 10\)

Step3: Solve \(10x + 4 = 20\)

Subtract 4: \(10x + 4 - 4 = 20 - 4\) → \(10x = 16\)
Divide by 10: \(x = \frac{16}{10} = \frac{8}{5}\)

Step4: Solve \(6x + 2 = 2x - 1\)

Subtract \(2x\): \(6x - 2x + 2 = -1\) → \(4x + 2 = -1\)
Subtract 2: \(4x = -3\)
Divide by 4: \(x = -\frac{3}{4}\)

Step5: Solve \(\frac{3}{4}x - 4 = 2\)

Add 4: \(\frac{3}{4}x - 4 + 4 = 2 + 4\) → \(\frac{3}{4}x = 6\)
Multiply by \(\frac{4}{3}\): \(x = 6\times\frac{4}{3}\) → \(x = 8\)

Step6: Solve \(3x + 4 = 2x - 6\)

Subtract \(2x\): \(3x - 2x + 4 = -6\) → \(x + 4 = -6\)
Subtract 4: \(x = -10\)

Step7: Simplify \(3(4x + 4x - x)\)

Combine like terms: \(3(7x)\) → \(21x\)

Step8: Simplify \(-4(10 - 2x) + 12 - 3x\)

Distribute: \(-40 + 8x + 12 - 3x\)
Combine like terms: \(5x - 28\)

Step9: Simplify \(7(9x + 4) + 6(x - 2)\)

Distribute: \(63x + 28 + 6x - 12\)
Combine like terms: \(69x + 16\)

Step10: Simplify \(6(7x + 5y) - 2y + 9x\)

Distribute: \(42x + 30y - 2y + 9x\)
Combine like terms: \(51x + 28y\)

Step11: Simplify \(-3(2x + 1)\)

Distribute: \(-6x - 3\)

Step12: Simplify \(5 - 2(x + 6)\)

Distribute: \(5 - 2x - 12\)
Combine like terms: \(-2x - 7\)

Answer:

1. \(21x\)
2. \(5x - 28\)
3. \(69x + 16\)
4. \(51x + 28y\)
5. \(-6x - 3\)
6. \(-2x - 7\)
7. \(x = -4\)
8. \(x = 10\)
9. \(x = \frac{8}{5}\)
10. \(x = -\frac{3}{4}\)
11. \(x = 8\)
12. \(x = -10\)