Question

2 solve each equation and check your solution.
-3w - 4 = w + 3
3(3 - 3x) = 2(x + 3) - 30
\frac{1}{3}(z + 4) - 6 = \frac{2}{3}(5 - z)

Explanation:

First Equation: \(-3w - 4 = w + 3\)

Step1: Move \(w\) terms to left and constants to right

Subtract \(w\) from both sides: \(-3w - w - 4 = 3\)
Add 4 to both sides: \(-4w = 3 + 4\)

Step2: Simplify and solve for \(w\)

Simplify right side: \(-4w = 7\)
Divide by \(-4\): \(w = -\frac{7}{4}\)

Step3: Check solution

Left: \(-3(-\frac{7}{4}) - 4 = \frac{21}{4} - \frac{16}{4} = \frac{5}{4}\)
Right: \(-\frac{7}{4} + 3 = -\frac{7}{4} + \frac{12}{4} = \frac{5}{4}\)
Left = Right, so \(w = -\frac{7}{4}\) is correct.

Second Equation: \(3(3 - 3x) = 2(x + 3) - 30\)

Step1: Expand both sides

Left: \(9 - 9x\)
Right: \(2x + 6 - 30 = 2x - 24\)

Step2: Move \(x\) terms to left and constants to right

Add \(9x\) to both sides: \(9 = 11x - 24\)
Add 24 to both sides: \(33 = 11x\)

Step3: Solve for \(x\)

Divide by 11: \(x = 3\)

Step4: Check solution

Left: \(3(3 - 9) = 3(-6) = -18\)
Right: \(2(6) - 30 = 12 - 30 = -18\)
Left = Right, so \(x = 3\) is correct.

Third Equation: \(\frac{1}{3}(z + 4) - 6 = \frac{2}{3}(5 - z)\)

Step1: Eliminate denominators (multiply by 3)

\(z + 4 - 18 = 2(5 - z)\)

Step2: Simplify both sides

Left: \(z - 14\)
Right: \(10 - 2z\)

Step3: Move \(z\) terms to left and constants to right

Add \(2z\) to both sides: \(3z - 14 = 10\)
Add 14 to both sides: \(3z = 24\)

Step4: Solve for \(z\)

Divide by 3: \(z = 8\)

Step5: Check solution

Left: \(\frac{1}{3}(12) - 6 = 4 - 6 = -2\)
Right: \(\frac{2}{3}(-3) = -2\)
Left = Right, so \(z = 8\) is correct.

Answer:

s:
\(w = \boldsymbol{-\frac{7}{4}}\), \(x = \boldsymbol{3}\), \(z = \boldsymbol{8}\)