Solved on Jan 23, 2024

Arrange the steps to solve the equation $\frac{1}{4}(x-1)+3x=2$ .

STEP 1

Assumptions
1. We are given an equation with an unknown variable $x$ .
2. We need to solve for $x$ .
3. The equation is linear.

STEP 2

Identify the original equation from the given options.
$\frac{1}{4}(x-1)+3x=2$
This is the original equation that we will be solving.

STEP 3

Distribute the $\frac{1}{4}$ across the terms inside the parentheses.
$\frac{1}{4}x - \frac{1}{4} + 3x = 2$
This step simplifies the left-hand side of the equation.

STEP 4

Combine like terms on the left-hand side of the equation.
$\frac{1}{4}x + 3x = \frac{1}{4}x + \frac{12}{4}x = \frac{13}{4}x$
So, the equation becomes:
$\frac{13}{4}x - \frac{1}{4} = 2$

STEP 5

Add $\frac{1}{4}$ to both sides of the equation to isolate the term with $x$ on the left-hand side.
$\frac{13}{4}x - \frac{1}{4} + \frac{1}{4} = 2 + \frac{1}{4}$

STEP 6

Simplify both sides of the equation.
$\frac{13}{4}x = \frac{9}{4}$

STEP 7

Multiply both sides of the equation by the reciprocal of $\frac{13}{4}$ to solve for $x$ .
$x = \frac{9}{4} \cdot \frac{4}{13}$

STEP 8

Simplify the right-hand side to find the value of $x$ .
$x = \frac{9 \cdot 4}{4 \cdot 13} = \frac{9}{13}$
Now, let's arrange the correct order of the solution steps:
1. The original equation: $\frac{1}{4}(x-1)+3x=2$
2. Distribute the fraction: $\frac{1}{4}x - \frac{1}{4} + 3x = 2$
3. Combine like terms: $\frac{13}{4}x - \frac{1}{4} = 2$
4. Add $\frac{1}{4}$ to both sides: $\frac{13}{4}x = \frac{9}{4}$
So the correct order is:
$\begin{array}{l} \frac{1}{4}(x-1)+3x=2 \\ \equiv \frac{1}{4}x-\frac{1}{4}+3x=2 \\ \equiv \frac{13}{4}x-\frac{1}{4}=2 \\ \equiv \frac{13}{4}x=\frac{9}{4} \end{array}$

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Arrange the steps to solve the equation $\frac{1}{4}(x-1)+3x=2$ .

STEP 1

Assumptions
1. We are given an equation with an unknown variable $x$ .
2. We need to solve for $x$ .
3. The equation is linear.

STEP 2

Identify the original equation from the given options.
$\frac{1}{4}(x-1)+3x=2$
This is the original equation that we will be solving.

STEP 3

Distribute the $\frac{1}{4}$ across the terms inside the parentheses.
$\frac{1}{4}x - \frac{1}{4} + 3x = 2$
This step simplifies the left-hand side of the equation.

STEP 4

Combine like terms on the left-hand side of the equation.
$\frac{1}{4}x + 3x = \frac{1}{4}x + \frac{12}{4}x = \frac{13}{4}x$
So, the equation becomes:
$\frac{13}{4}x - \frac{1}{4} = 2$

STEP 5

Add $\frac{1}{4}$ to both sides of the equation to isolate the term with $x$ on the left-hand side.
$\frac{13}{4}x - \frac{1}{4} + \frac{1}{4} = 2 + \frac{1}{4}$

STEP 6

Simplify both sides of the equation.
$\frac{13}{4}x = \frac{9}{4}$

STEP 7

Multiply both sides of the equation by the reciprocal of $\frac{13}{4}$ to solve for $x$ .
$x = \frac{9}{4} \cdot \frac{4}{13}$

STEP 8

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Arrange the steps to solve the equation 14(x−1)+3x=2\frac{1}{4}(x-1)+3x=241​(x−1)+3x=2.

STEP 1

Assumptions1. We are given an equation with an unknown variable xxx.2. We need to solve for xxx.3. The equation is linear.

STEP 2

Identify the original equation from the given options.14(x−1)+3x=2\frac{1}{4}(x-1)+3x=241​(x−1)+3x=2This is the original equation that we will be solving.

STEP 3

Distribute the 14\frac{1}{4}41​ across the terms inside the parentheses.14x−14+3x=2\frac{1}{4}x - \frac{1}{4} + 3x = 241​x−41​+3x=2This step simplifies the left-hand side of the equation.

STEP 4

Combine like terms on the left-hand side of the equation.14x+3x=14x+124x=134x\frac{1}{4}x + 3x = \frac{1}{4}x + \frac{12}{4}x = \frac{13}{4}x41​x+3x=41​x+412​x=413​xSo, the equation becomes:134x−14=2\frac{13}{4}x - \frac{1}{4} = 2413​x−41​=2

STEP 5

Add 14\frac{1}{4}41​ to both sides of the equation to isolate the term with xxx on the left-hand side.134x−14+14=2+14\frac{13}{4}x - \frac{1}{4} + \frac{1}{4} = 2 + \frac{1}{4}413​x−41​+41​=2+41​

STEP 6

Simplify both sides of the equation.134x=94\frac{13}{4}x = \frac{9}{4}413​x=49​

STEP 7

Multiply both sides of the equation by the reciprocal of 134\frac{13}{4}413​ to solve for xxx.x=94⋅413x = \frac{9}{4} \cdot \frac{4}{13}x=49​⋅134​

STEP 8

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Arrange the steps to solve the equation $\frac{1}{4}(x-1)+3x=2$ .

Assumptions
1. We are given an equation with an unknown variable $x$ .
2. We need to solve for $x$ .
3. The equation is linear.

Identify the original equation from the given options.
$\frac{1}{4}(x-1)+3x=2$
This is the original equation that we will be solving.

Distribute the $\frac{1}{4}$ across the terms inside the parentheses.
$\frac{1}{4}x - \frac{1}{4} + 3x = 2$
This step simplifies the left-hand side of the equation.

Combine like terms on the left-hand side of the equation.
$\frac{1}{4}x + 3x = \frac{1}{4}x + \frac{12}{4}x = \frac{13}{4}x$
So, the equation becomes:
$\frac{13}{4}x - \frac{1}{4} = 2$

Add $\frac{1}{4}$ to both sides of the equation to isolate the term with $x$ on the left-hand side.
$\frac{13}{4}x - \frac{1}{4} + \frac{1}{4} = 2 + \frac{1}{4}$

Simplify both sides of the equation.
$\frac{13}{4}x = \frac{9}{4}$

Multiply both sides of the equation by the reciprocal of $\frac{13}{4}$ to solve for $x$ .
$x = \frac{9}{4} \cdot \frac{4}{13}$