Solved on Jan 01, 2024

Solve one-step equations without cross-multiplying: (a) $7x=84$ , (b) $\frac{x}{3}=15$ , (c) $\frac{x}{9}=\frac{2}{3}$ .

STEP 1

Assumptions
1. The equations given are one-step equations.
2. Cross multiplying is not necessary or allowed for solving these equations.
3. The goal is to isolate the variable $x$ on one side of the equation.

STEP 2

Solve equation (a) $7x = 84$ .
To isolate $x$ , we need to divide both sides of the equation by the coefficient of $x$ , which is 7.
$x = \frac{84}{7}$

STEP 3

Calculate the value of $x$ for equation (a).
$x = \frac{84}{7} = 12$

STEP 4

Solve equation (b) $\frac{x}{3} = 15$ .
To isolate $x$ , we need to multiply both sides of the equation by the denominator of the fraction, which is 3.
$x = 15 \times 3$

STEP 5

Calculate the value of $x$ for equation (b).
$x = 15 \times 3 = 45$

STEP 6

Solve equation (c) $\frac{x}{9} = \frac{2}{3}$ .
To isolate $x$ , we need to multiply both sides of the equation by the denominator of the fraction on the left side, which is 9.
$x = \frac{2}{3} \times 9$

STEP 7

Calculate the value of $x$ for equation (c).
Since $\frac{2}{3} \times 9$ is the same as $2 \times \frac{9}{3}$ , we can simplify the fraction first.
$x = 2 \times \frac{9}{3}$

STEP 8

Simplify the fraction and calculate the value of $x$ for equation (c).
$x = 2 \times 3 = 6$
The solutions are: (a) $x = 12$ (b) $x = 45$ (c) $x = 6$

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Solve one-step equations without cross-multiplying: (a) $7x=84$ , (b) $\frac{x}{3}=15$ , (c) $\frac{x}{9}=\frac{2}{3}$ .

STEP 1

Assumptions
1. The equations given are one-step equations.
2. Cross multiplying is not necessary or allowed for solving these equations.
3. The goal is to isolate the variable $x$ on one side of the equation.

STEP 2

Solve equation (a) $7x = 84$ .
To isolate $x$ , we need to divide both sides of the equation by the coefficient of $x$ , which is 7.
$x = \frac{84}{7}$

STEP 3

Calculate the value of $x$ for equation (a).
$x = \frac{84}{7} = 12$

STEP 4

Solve equation (b) $\frac{x}{3} = 15$ .
To isolate $x$ , we need to multiply both sides of the equation by the denominator of the fraction, which is 3.
$x = 15 \times 3$

STEP 5

Calculate the value of $x$ for equation (b).
$x = 15 \times 3 = 45$

STEP 6

Solve equation (c) $\frac{x}{9} = \frac{2}{3}$ .
To isolate $x$ , we need to multiply both sides of the equation by the denominator of the fraction on the left side, which is 9.
$x = \frac{2}{3} \times 9$

STEP 7

Calculate the value of $x$ for equation (c).
Since $\frac{2}{3} \times 9$ is the same as $2 \times \frac{9}{3}$ , we can simplify the fraction first.
$x = 2 \times \frac{9}{3}$

STEP 8

Simplify the fraction and calculate the value of $x$ for equation (c).
$x = 2 \times 3 = 6$
The solutions are: (a) $x = 12$ (b) $x = 45$ (c) $x = 6$

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Solve one-step equations without cross-multiplying: (a) 7x=847x=847x=84, (b) x3=15\frac{x}{3}=153x​=15, (c) x9=23\frac{x}{9}=\frac{2}{3}9x​=32​.

STEP 1

Assumptions1. The equations given are one-step equations.2. Cross multiplying is not necessary or allowed for solving these equations.3. The goal is to isolate the variable xxx on one side of the equation.

STEP 2

Solve equation (a) 7x=847x = 847x=84.To isolate xxx, we need to divide both sides of the equation by the coefficient of xxx, which is 7.x=847x = \frac{84}{7}x=784​

STEP 3

Calculate the value of xxx for equation (a).x=847=12x = \frac{84}{7} = 12x=784​=12

STEP 4

Solve equation (b) x3=15\frac{x}{3} = 153x​=15.To isolate xxx, we need to multiply both sides of the equation by the denominator of the fraction, which is 3.x=15×3x = 15 \times 3x=15×3

STEP 5

Calculate the value of xxx for equation (b).x=15×3=45x = 15 \times 3 = 45x=15×3=45

STEP 6

Solve equation (c) x9=23\frac{x}{9} = \frac{2}{3}9x​=32​.To isolate xxx, we need to multiply both sides of the equation by the denominator of the fraction on the left side, which is 9.x=23×9x = \frac{2}{3} \times 9x=32​×9

STEP 7

Calculate the value of xxx for equation (c).Since 23×9\frac{2}{3} \times 932​×9 is the same as 2×932 \times \frac{9}{3}2×39​, we can simplify the fraction first.x=2×93x = 2 \times \frac{9}{3}x=2×39​

STEP 8

Simplify the fraction and calculate the value of xxx for equation (c).x=2×3=6x = 2 \times 3 = 6x=2×3=6The solutions are: (a) x=12x = 12x=12 (b) x=45x = 45x=45 (c) x=6x = 6x=6

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Solve one-step equations without cross-multiplying: (a) $7x=84$ , (b) $\frac{x}{3}=15$ , (c) $\frac{x}{9}=\frac{2}{3}$ .

Assumptions
1. The equations given are one-step equations.
2. Cross multiplying is not necessary or allowed for solving these equations.
3. The goal is to isolate the variable $x$ on one side of the equation.

Solve equation (a) $7x = 84$ .
To isolate $x$ , we need to divide both sides of the equation by the coefficient of $x$ , which is 7.
$x = \frac{84}{7}$

Calculate the value of $x$ for equation (a).
$x = \frac{84}{7} = 12$

Solve equation (b) $\frac{x}{3} = 15$ .
To isolate $x$ , we need to multiply both sides of the equation by the denominator of the fraction, which is 3.
$x = 15 \times 3$

Calculate the value of $x$ for equation (b).
$x = 15 \times 3 = 45$

Solve equation (c) $\frac{x}{9} = \frac{2}{3}$ .
To isolate $x$ , we need to multiply both sides of the equation by the denominator of the fraction on the left side, which is 9.
$x = \frac{2}{3} \times 9$

Calculate the value of $x$ for equation (c).
Since $\frac{2}{3} \times 9$ is the same as $2 \times \frac{9}{3}$ , we can simplify the fraction first.
$x = 2 \times \frac{9}{3}$

Simplify the fraction and calculate the value of $x$ for equation (c).
$x = 2 \times 3 = 6$
The solutions are: (a) $x = 12$ (b) $x = 45$ (c) $x = 6$