QuestionSolve the linear equation: $\frac{6 z-4}{4}+\frac{13}{8}=\frac{12 z+1}{8}$ .

Studdy Solution

STEP 1

Assumptions1. We are given a linear equation in the form of fractions. . The variable in the equation is $z$ .
3. We are asked to solve for $z$ .

STEP 2

First, let's simplify the equation by multiplying each term by8 to eliminate the denominators.
$8 \times \left(\frac{6 z-4}{4}\right) +8 \times \left(\frac{13}{8}\right) =8 \times \left(\frac{12 z+1}{8}\right)$

STEP 3

implify each term.
$2 \times (6 z-) +13 =12 z+1$

STEP 4

Expand the left side of the equation.
$12 z -8 +13 =12 z +1$

STEP 5

implify the left side of the equation.
$12 z +5 =12 z +1$

STEP 6

Subtract $12 z$ from both sides of the equation to isolate the variable $z$ on one side.
$12 z +5 -12 z =12 z +1 -12 z$

STEP 7

implify both sides of the equation.
$5 =1$

STEP 8

At this point, we see that the equation is not true. This implies that the original equation has no solution.
The solution to the equation is that there is no solution.

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QuestionSolve the linear equation: $\frac{6 z-4}{4}+\frac{13}{8}=\frac{12 z+1}{8}$ .

Studdy Solution

STEP 1

Assumptions1. We are given a linear equation in the form of fractions. . The variable in the equation is $z$ .
3. We are asked to solve for $z$ .

STEP 2

First, let's simplify the equation by multiplying each term by8 to eliminate the denominators.
$8 \times \left(\frac{6 z-4}{4}\right) +8 \times \left(\frac{13}{8}\right) =8 \times \left(\frac{12 z+1}{8}\right)$

STEP 3

implify each term.
$2 \times (6 z-) +13 =12 z+1$

STEP 4

Expand the left side of the equation.
$12 z -8 +13 =12 z +1$

STEP 5

implify the left side of the equation.
$12 z +5 =12 z +1$

STEP 6

Subtract $12 z$ from both sides of the equation to isolate the variable $z$ on one side.
$12 z +5 -12 z =12 z +1 -12 z$

STEP 7

implify both sides of the equation.
$5 =1$

STEP 8

At this point, we see that the equation is not true. This implies that the original equation has no solution.
The solution to the equation is that there is no solution.

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QuestionSolve the linear equation: 6z−44+138=12z+18\frac{6 z-4}{4}+\frac{13}{8}=\frac{12 z+1}{8}46z−4​+813​=812z+1​.

Studdy Solution

STEP 1

Assumptions1. We are given a linear equation in the form of fractions. . The variable in the equation is zzz.3. We are asked to solve for zzz.

STEP 2

First, let's simplify the equation by multiplying each term by8 to eliminate the denominators.8×(6z−44)+8×(138)=8×(12z+18)8 \times \left(\frac{6 z-4}{4}\right) +8 \times \left(\frac{13}{8}\right) =8 \times \left(\frac{12 z+1}{8}\right)8×(46z−4​)+8×(813​)=8×(812z+1​)

STEP 3

implify each term.2×(6z−)+13=12z+12 \times (6 z-) +13 =12 z+12×(6z−)+13=12z+1

STEP 4

Expand the left side of the equation.12z−8+13=12z+112 z -8 +13 =12 z +112z−8+13=12z+1

STEP 5

implify the left side of the equation.12z+5=12z+112 z +5 =12 z +112z+5=12z+1

STEP 6

Subtract 12z12 z12z from both sides of the equation to isolate the variable zzz on one side.12z+5−12z=12z+1−12z12 z +5 -12 z =12 z +1 -12 z12z+5−12z=12z+1−12z

STEP 7

implify both sides of the equation.5=15 =15=1

STEP 8

At this point, we see that the equation is not true. This implies that the original equation has no solution.The solution to the equation is that there is no solution.

Get Studdy

Studdy solves anything!

Start learning now

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

QuestionSolve the linear equation: $\frac{6 z-4}{4}+\frac{13}{8}=\frac{12 z+1}{8}$ .

Assumptions1. We are given a linear equation in the form of fractions. . The variable in the equation is $z$ .
3. We are asked to solve for $z$ .

First, let's simplify the equation by multiplying each term by8 to eliminate the denominators.
$8 \times \left(\frac{6 z-4}{4}\right) +8 \times \left(\frac{13}{8}\right) =8 \times \left(\frac{12 z+1}{8}\right)$

implify each term.
$2 \times (6 z-) +13 =12 z+1$

Expand the left side of the equation.
$12 z -8 +13 =12 z +1$

implify the left side of the equation.
$12 z +5 =12 z +1$

Subtract $12 z$ from both sides of the equation to isolate the variable $z$ on one side.
$12 z +5 -12 z =12 z +1 -12 z$

implify both sides of the equation.
$5 =1$

At this point, we see that the equation is not true. This implies that the original equation has no solution.
The solution to the equation is that there is no solution.