QuestionFind $x$ for these equations: a) $\frac{x}{2}-7=14$ b) $\frac{6 x}{8}+3=-7$ c) $\frac{8}{x}+4=9.10 \times 10^{-2}$ d) $\frac{3}{4 x}-1.5=2.70 \times 10^{3}$ .

Studdy Solution

STEP 1

Assumptions1. For each expression, we are solving for the variable $x$ . . The operations involved are addition, subtraction, multiplication, and division.
3. We will use the principles of algebra to isolate $x$ on one side of the equation.

STEP 2

Let's start with the first equation $\frac{x}{2}-7=14$
To isolate $x$ , we first need to get rid of the $-7$ on the left side of the equation. We can do this by adding $7$ to both sides of the equation.
$\frac{x}{2}-7+7=14+7$

STEP 3

implify the equation.
$\frac{x}{2}=21$

STEP 4

Now, to solve for $x$ , we need to get rid of the fraction. We can do this by multiplying both sides of the equation by $2$ .
$2 \times \frac{x}{2}=21 \times2$

STEP 5

implify the equation.
$x=42$ So, for the first equation, $x=42$ .

STEP 6

Now, let's move on to the second equation $\frac{6x}{8}+3=-$
First, we need to get rid of the $+3$ on the left side of the equation. We can do this by subtracting $3$ from both sides of the equation.
$\frac{6x}{8}+3-3=--3$

STEP 7

implify the equation.
$\frac{6x}{}=-10$

STEP 8

Now, to solve for $x$ , we need to get rid of the fraction. We can do this by multiplying both sides of the equation by $8$ .
$8 \times \frac{6x}{8}=-10 \times8$

STEP 9

implify the equation.
$6x=-80$

STEP 10

Finally, to solve for $x$ , we divide both sides of the equation by $6$ .
$x=\frac{-80}{6}$

STEP 11

implify the equation.
$x=-\frac{40}{3}$ So, for the second equation, $x=-\frac{40}{3}$ .

STEP 12

Now, let's move on to the third equation $\frac{8}{x}+4=9.10 \times10^{-2}$ First, we need to get rid of the $+4$ on the left side of the equation. We can do this by subtracting $4$ from both sides of the equation.
$\frac{8}{x}+4-4=9.10 \times10^{-2}-4$

STEP 13

implify the equation.
$\frac{8}{x}=-3.991$

STEP 14

Now, to solve for $x$ , we need to get rid of the fraction. We can do this by multiplying both sides of the equation by $x$ and then dividing by the number on the right side of the equation.
$x=\frac{8}{-3.991}$

STEP 15

implify the equation.
$x=-2.004$ So, for the third equation, $x=-2.004$ .

STEP 16

Finally, let's move on to the fourth equation $\frac{3}{4x}-.5=2.70 \times10^{3}$ First, we need to get rid of the $-.5$ on the left side of the equation. We can do this by adding $.5$ to both sides of the equation.
$\frac{3}{4x}-.5+.5=2.70 \times10^{3}+.5$

STEP 17

implify the equation.
$\frac{3}{4x}=270.5$

STEP 18

Now, to solve for $x$ , we need to get rid of the fraction. We can do this by multiplying both sides of the equation by $4x$ and then dividing by the number on the right side of the equation.
$x=\frac{3}{270.5 \times4}$

STEP 19

implify the equation.
$x=.78 \times10^{-4}$ So, for the fourth equation, $x=.78 \times10^{-4}$ .

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