Question

assignment: page 348
solve each equation.
ⓐ \\(\frac{2}{3}(x + 2) = \frac{1}{6}x + \frac{1}{3}\\) ⓑ \\(2.5x - 1 = 10 - 7.5x\\)
ⓒ \\(7x - 3 = 3 + 6x\\) ⓓ \\(x + 2 = -14 - x\\)
11 numeric 1 point
a. \\(x = \underline{\quad}\\)
answer
\\(\boxed{}\\)
12 numeric 1 point
b. \\(x = \underline{\quad}\\)
answer
\\(\boxed{}\\)

Explanation:

Part a: Solve \(\boldsymbol{\frac{2}{3}(x + 2)=\frac{1}{6}x+\frac{1}{3}}\)

Step1: Eliminate denominators (multiply by 6)

\(6\times\frac{2}{3}(x + 2)=6\times\frac{1}{6}x+6\times\frac{1}{3}\)
\(4(x + 2)=x + 2\)

Step2: Expand left side

\(4x+8=x + 2\)

Step3: Subtract \(x\) from both sides

\(4x - x+8=x - x + 2\)
\(3x+8=2\)

Step4: Subtract 8 from both sides

\(3x+8 - 8=2 - 8\)
\(3x=-6\)

Step5: Divide by 3

\(\frac{3x}{3}=\frac{-6}{3}\)
\(x=-2\)

Part b: Solve \(\boldsymbol{2.5x - 1=10 - 7.5x}\)

Step1: Add \(7.5x\) to both sides

\(2.5x+7.5x - 1=10 - 7.5x+7.5x\)
\(10x - 1=10\)

Step2: Add 1 to both sides

\(10x - 1+1=10+1\)
\(10x=11\)

Step3: Divide by 10

\(\frac{10x}{10}=\frac{11}{10}\)
\(x = 1.1\)

Part c: Solve \(\boldsymbol{7x - 3=3 + 6x}\)

Step1: Subtract \(6x\) from both sides

\(7x - 6x - 3=3 + 6x - 6x\)
\(x - 3=3\)

Step2: Add 3 to both sides

\(x - 3+3=3+3\)
\(x=6\)

Part d: Solve \(\boldsymbol{x + 2=-14 - x}\)

Answer:

s:
a. \(x = -2\)
b. \(x = 1.1\)
c. \(x = 6\)
d. \(x = -8\)