Question

quiz chapter 2
show all work and circle your answers.

1. solve the following: $\frac{3t}{4}-\frac{t}{2}=1$
2. solve the following: $0.6x - 10 = 1.4x - 14$

Explanation:

Step1: Find common - denominator for the first equation

The common denominator of 4 and 2 is 4. Rewrite $\frac{t}{2}$ as $\frac{2t}{4}$. So the equation $\frac{3t}{4}-\frac{t}{2}=1$ becomes $\frac{3t}{4}-\frac{2t}{4}=1$.

Step2: Combine like - terms

$\frac{3t - 2t}{4}=1$, which simplifies to $\frac{t}{4}=1$.

Step3: Solve for t

Multiply both sides of the equation $\frac{t}{4}=1$ by 4. We get $t = 4$.

Step4: Solve the second equation

Start with $0.6x-10 = 1.4x-14$. First, subtract $0.6x$ from both sides:
$-10=1.4x - 0.6x-14$.

Step5: Combine like - terms

$-10 = 0.8x-14$.

Step6: Add 14 to both sides

$-10 + 14=0.8x$, so $4 = 0.8x$.

Step7: Solve for x

Divide both sides by 0.8. $x=\frac{4}{0.8}=5$.

Answer:

1. $t = 4$
2. $x = 5$