Question

Solve and check. $$-\frac{5}{6}=x-\frac{1}{4}$$

   Solve and check.
$$-\frac{5}{6}=x-\frac{1}{4}$$

Prealgebra and Introductory Algebra

Prealgebra and Introductory Algebra

Richard N. Aufmann,… 3rd Edition

Chapter 5, Problem 55

Instant Answer

Solved by Expert Ethan Somes

06/21/2020

Step 1

Step 1: We start with the equation $$-\frac{5}{6}=x-\frac{1}{4}$$ We want to isolate x, so we add $\frac{1}{4}$ to both sides of the equation. Show more…

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Solve and check. $$-\frac{5}{6}=x-\frac{1}{4}$$

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Key Concepts

Verification of Solutions

Checking a solution involves substituting the found value back into the original equation to confirm that both sides are equal. This verification step is crucial for ensuring the correctness of the solution.

Linear Equations

Linear equations are equations where the variable is raised only to the first power and their graphs form straight lines. The goal in solving a linear equation is to isolate the variable on one side of the equation, which is a fundamental technique in algebra.

Inverse Operations

Inverse operations are used to 'undo' operations in an equation, allowing you to isolate the variable. In solving a linear equation, performing the opposite operation on both sides ensures that the equality is maintained while systematically isolating the variable.

Fraction Arithmetic

When dealing with fractions, it is essential to find common denominators and properly combine or separate fractional terms. This allows for accurate manipulation of terms when solving equations that involve fractions.

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Transcript

00:01 Here we have the equation negative 5, 6 equals x minus 1 fourth.

00:08 And we want to get x by itself, so we figure out what x is equal to.

00:12 So we want to undo whatever is happening to x.

00:15 Currently, we have x minus 1 fourth.

00:17 I'm going to do the opposite and add 1 fourth to both sides of the equation.

00:22 So that will give me, on this side of the equation, negative 5, 6 plus 1, 4th equals x, and then minus one -fourth plus one -fourth equals zero.

00:32 So x plus zero is just equal to x.

00:35 So now let's figure out what negative 5, 6 plus 1 -4th is.

00:40 So we want to find a common denominator for these two, so we can add them.

00:44 So i think of my least common multiple of 6 and 4.

00:49 6 and 4.

00:51 So if i think about skip counting here, we do 6, 12, 18, 24, et cetera.

00:58 We'll go further if we need to.

00:59 4, 8, 12, oh, here we go.

01:02 Our least common multiple is 12.

01:04 So i'm going to change these, both have a denominator of 12.

01:07 So negative 5, 6 equals some amount of 12s.

01:12 To do that, i'm going to multiply both the numerator and denominator by 2, and i get negative 10 twelts.

01:18 Because i multiplied by 2 over 2, that's the same as multiplying by 1, so i didn't change the value...

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