Question

solve the equation: $\frac{7}{8}x - 2 = 5$
a. $x = 6$
b. $x = 7$
c. $x = 5$
d. $x = 8$
solve the equation: $1.5x - 2.5 = 5$
a. $x = 4$
b. $x = 5$
c. $x = 3$
d. $x = 6$

Explanation:

First Equation: $\boldsymbol{\frac{1}{8}x - 2 = 5}$

Step1: Add 2 to both sides

To isolate the term with \( x \), we add 2 to both sides of the equation. This gives us \(\frac{1}{8}x - 2 + 2 = 5 + 2\), which simplifies to \(\frac{1}{8}x = 7\).

Step2: Multiply both sides by 8

To solve for \( x \), we multiply both sides of the equation \(\frac{1}{8}x = 7\) by 8. This gives us \( x = 7\times8 \), so \( x = 56 \)? Wait, no, wait, the original equation is \(\frac{1}{8}x - 2 = 5\)? Wait, the user's first equation: looking at the image, the first equation is \(\frac{1}{8}x - 2 = 5\)? Wait, no, the options are a. \( x = 6 \), b. \( x = 7 \), c. \( x = 5 \), d. \( x = 8 \). Wait, maybe I misread the equation. Wait, maybe the equation is \(\frac{1}{8}x\)? No, maybe it's \(\frac{7}{8}x\)? Wait, the user's image: "Solve the equation: 7/8 x - 2 = 5" (maybe a typo in my initial reading). Let's re-express.

Assuming the equation is \(\frac{7}{8}x - 2 = 5\) (since the options are small numbers, maybe a typo in the numerator). Wait, no, the options are x=6,7,5,8. Let's check with the given options. Wait, maybe the equation is \(\frac{1}{8}x\) is wrong. Wait, let's check the first equation again.

Wait, the first equation: "Solve the equation: 7/8 x - 2 = 5" (maybe the numerator is 7? But the options are x=6,7,5,8. Wait, no, maybe the equation is \(\frac{1}{8}x - 2 = 5\) is incorrect. Wait, let's check the options. If we test x=8: \(\frac{1}{8}\times8 - 2 = 1 - 2 = -1
eq 5\). x=7: \(\frac{1}{8}\times7 - 2 = 0.875 - 2 = -1.125
eq 5\). x=6: \(\frac{1}{8}\times6 - 2 = 0.75 - 2 = -1.25
eq 5\). x=5: \(\frac{1}{8}\times5 - 2 = 0.625 - 2 = -1.375
eq 5\). So there must be a misreading. Wait, maybe the equation is \(\frac{7}{8}x - 2 = 5\)? Let's solve that:

\(\frac{7}{8}x - 2 = 5\)

Step1: Add 2 to both sides: \(\frac{7}{8}x = 7\)

Step2: Multiply both sides by \(\frac{8}{7}\): \( x = 7\times\frac{8}{7} = 8 \). Ah! So the equation is \(\frac{7}{8}x - 2 = 5\), and the solution is x=8, which is option d.

Okay, so correcting the equation: \(\frac{7}{8}x - 2 = 5\)

(corrected):

Step1: Add 2 to both sides

\(\frac{7}{8}x - 2 + 2 = 5 + 2\)
\(\frac{7}{8}x = 7\)

Step2: Multiply by \(\frac{8}{7}\)

\( x = 7 \times \frac{8}{7} \)
\( x = 8 \)

Step1: Add 2.5 to both sides

To isolate the term with \( x \), add 2.5 to both sides: \( 1.5x - 2.5 + 2.5 = 5 + 2.5 \), which simplifies to \( 1.5x = 7.5 \).

Step2: Divide by 1.5

To solve for \( x \), divide both sides by 1.5: \( x = \frac{7.5}{1.5} \), so \( x = 5 \).

Answer:

(first equation):
d. \( x = 8 \)

Second Equation: $\boldsymbol{1.5x - 2.5 = 5}$