Solved on Sep 12, 2023

Solve for $x$ in the equation $\frac{2 x}{3} + 2 = 10$ .

STEP 1

Assumptions1. The equation to solve is $\frac{x}{3} + =10$ . We are solving for $x$

STEP 2

First, we need to isolate the term with $x$ on one side of the equation. We can do this by subtracting2 from both sides of the equation.
$\frac{2x}{} +2 -2 =10 -2$

STEP 3

implify the equation.
$\frac{2x}{3} =10 -2$

STEP 4

Calculate the right side of the equation.
$\frac{2x}{3} =8$

STEP 5

To solve for $x$ , we need to get rid of the fraction. We can do this by multiplying both sides of the equation by the reciprocal of $\frac{2}{3}$ , which is $\frac{3}{2}$ .
$\frac{2x}{3} \times \frac{3}{2} =8 \times \frac{3}{2}$

STEP 6

implify the left side of the equation.
$x =8 \times \frac{3}{2}$

STEP 7

Calculate the right side of the equation.
$x = \times \frac{3}{2} =12$ So, the solution to the equation is $x =12$ .

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Solve for $x$ in the equation $\frac{2 x}{3} + 2 = 10$ .

STEP 1

Assumptions1. The equation to solve is $\frac{x}{3} + =10$ . We are solving for $x$

STEP 2

First, we need to isolate the term with $x$ on one side of the equation. We can do this by subtracting2 from both sides of the equation.
$\frac{2x}{} +2 -2 =10 -2$

STEP 3

implify the equation.
$\frac{2x}{3} =10 -2$

STEP 4

Calculate the right side of the equation.
$\frac{2x}{3} =8$

STEP 5

To solve for $x$ , we need to get rid of the fraction. We can do this by multiplying both sides of the equation by the reciprocal of $\frac{2}{3}$ , which is $\frac{3}{2}$ .
$\frac{2x}{3} \times \frac{3}{2} =8 \times \frac{3}{2}$

STEP 6

implify the left side of the equation.
$x =8 \times \frac{3}{2}$

STEP 7

Calculate the right side of the equation.
$x = \times \frac{3}{2} =12$ So, the solution to the equation is $x =12$ .

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Solve for xxx in the equation 2x3+2=10\frac{2 x}{3} + 2 = 1032x​+2=10.

STEP 1

Assumptions1. The equation to solve is x3+=10\frac{x}{3} + =103x​+=10 . We are solving for xxx

STEP 2

First, we need to isolate the term with xxx on one side of the equation. We can do this by subtracting2 from both sides of the equation.2x+2−2=10−2\frac{2x}{} +2 -2 =10 -22x​+2−2=10−2

STEP 3

implify the equation.2x3=10−2\frac{2x}{3} =10 -232x​=10−2

STEP 4

Calculate the right side of the equation.2x3=8\frac{2x}{3} =832x​=8

STEP 5

To solve for xxx, we need to get rid of the fraction. We can do this by multiplying both sides of the equation by the reciprocal of 23\frac{2}{3}32​, which is 32\frac{3}{2}23​.2x3×32=8×32\frac{2x}{3} \times \frac{3}{2} =8 \times \frac{3}{2}32x​×23​=8×23​

STEP 6

implify the left side of the equation.x=8×32x =8 \times \frac{3}{2}x=8×23​

STEP 7

Calculate the right side of the equation.x=×32=12x = \times \frac{3}{2} =12x=×23​=12So, the solution to the equation is x=12x =12x=12.

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Solve for $x$ in the equation $\frac{2 x}{3} + 2 = 10$ .

Assumptions1. The equation to solve is $\frac{x}{3} + =10$ . We are solving for $x$

First, we need to isolate the term with $x$ on one side of the equation. We can do this by subtracting2 from both sides of the equation.
$\frac{2x}{} +2 -2 =10 -2$

implify the equation.
$\frac{2x}{3} =10 -2$

Calculate the right side of the equation.
$\frac{2x}{3} =8$

To solve for $x$ , we need to get rid of the fraction. We can do this by multiplying both sides of the equation by the reciprocal of $\frac{2}{3}$ , which is $\frac{3}{2}$ .
$\frac{2x}{3} \times \frac{3}{2} =8 \times \frac{3}{2}$

implify the left side of the equation.
$x =8 \times \frac{3}{2}$

Calculate the right side of the equation.
$x = \times \frac{3}{2} =12$ So, the solution to the equation is $x =12$ .