Question

solve the equation: $\frac{4}{7}x + 1 = 5$
a. $x = 5$
b. $x = 3$
c. $x = 6$
d. $x = 7$
solve the equation: $0.6x - 1.2 = 3$
a. $x = 7$
b. $x = 2$
c. $x = 4$
d. $x = 5$

Explanation:

First Equation: $\boldsymbol{\frac{4}{7}x + 1 = 5}$

Step1: Subtract 1 from both sides

$\frac{4}{7}x + 1 - 1 = 5 - 1$
$\frac{4}{7}x = 4$

Step2: Multiply both sides by $\frac{7}{4}$

$\frac{4}{7}x \times \frac{7}{4} = 4 \times \frac{7}{4}$
$x = 7$ (Wait, no—wait, 4 times 7/4 is 7? Wait, no: 4(7/4) = 7? Wait, 4 divided by 4 is 1, 17 is 7. But let's check the options. Wait, the options are a.5, b.3, c.6, d.7. Wait, maybe I made a mistake. Wait, let's re-calculate:

Wait, original equation: $\frac{4}{7}x + 1 = 5$

Subtract 1: $\frac{4}{7}x = 4$

Multiply both sides by $\frac{7}{4}$: $x = 4 \times \frac{7}{4} = 7$. So d. $x=7$ is correct.

Second Equation: $\boldsymbol{0.6x - 1.2 = 3}$

Step1: Add 1.2 to both sides

$0.6x - 1.2 + 1.2 = 3 + 1.2$
$0.6x = 4.2$

Step2: Divide both sides by 0.6

$x = \frac{4.2}{0.6}$
$x = 7$? Wait, no—4.2 divided by 0.6: 0.6*7=4.2, so x=7? But the options for the second equation are a.7, b.2, c.4, d.5. So a. $x=7$? Wait, no—wait, 0.6x -1.2=3. Let's check:

0.6x = 3 +1.2=4.2. Then x=4.2/0.6=7. So a. $x=7$ is correct. Wait, but let's recheck the first equation.

Wait, first equation: $\frac{4}{7}x +1=5$. Subtract 1: $\frac{4}{7}x=4$. Multiply by 7/4: x=4*(7/4)=7. So first equation answer is d. $x=7$, second is a. $x=7$? Wait, but the first equation's options: d is x=7. Second equation's options: a is x=7.

Wait, let's verify first equation: $\frac{4}{7}(7) +1 = 4 +1=5$. Correct. Second equation: 0.6(7) -1.2=4.2 -1.2=3. Correct.

Answer:

First equation: d. $x = 7$
Second equation: a. $x = 7$