Question

1. solve: $\frac{1}{2}x + 3 = 7$, $\frac{1}{2}x = 4$, circle: rational / irrational
2. solve: $4x-\frac{3}{5}=9$, circle: rational / irrational
3. solve: $3(x - \frac{2}{3}) = 5$, circle: rational / irrational
4. solve: $\frac{5}{6}x + 2=\frac{11}{6}$, circle: rational / irrational
5. solve: $2x + 7=\frac{15}{2}$, circle: rational / irrational
6. solve: $\frac{7}{8}x-4 = 2$, circle: rational / irrational
7. solve: $3x+\frac{1}{4}=\frac{19}{4}$, circle: rational / irrational
8. solve: $\frac{2}{3}(x - 5)=4$, circle: rational / irrational

Explanation:

1)

Step1: Isolate the term with x

Subtract 3 from both sides of $\frac{1}{2}x + 3=7$. We get $\frac{1}{2}x=7 - 3=4$.

Step2: Solve for x

Multiply both sides by 2. So $x = 4\times2=8$. Since 8 can be written as $\frac{8}{1}$, it is rational.

Step1: Isolate the term with x

Add $\frac{3}{5}$ to both sides of $4x-\frac{3}{5}=9$. We have $4x=9+\frac{3}{5}=\frac{45 + 3}{5}=\frac{48}{5}$.

Step2: Solve for x

Divide both sides by 4, $x=\frac{48}{5}\div4=\frac{48}{5}\times\frac{1}{4}=\frac{12}{5}$. Since $\frac{12}{5}$ is a fraction of two integers, it is rational.

Step1: Distribute the 3

$3(x-\frac{2}{3})=3x - 2=5$.

Step2: Isolate the term with x

Add 2 to both sides, $3x=5 + 2=7$.

Step3: Solve for x

Divide both sides by 3, $x=\frac{7}{3}$. Since $\frac{7}{3}$ is a ratio of two integers, it is rational.

Answer:

$x = 8$, Rational

2)