Problem 142 Solve the equations for the vari... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 8: Problem 142

Solve the equations for the variable. $$4 a+5=-a-40$$

Short Answer

Expert verified

a = -9

Step by step solution

Combine like terms

First, add $a$ on both sides to combine the variable terms. The equation becomes: \[4a + a + 5 = -40\] This simplifies to: \[5a + 5 = -40\]

Isolate the variable term

Next, subtract 5 from both sides to isolate the variable term on one side. The equation becomes: \[5a + 5 - 5 = -40 - 5\] This simplifies to: \[5a = -45\]

Solve for the variable

Finally, divide both sides by 5 to solve for the variable $a$. The equation becomes: \[a = \frac{-45}{5}\] This simplifies to: \[a = -9\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Combining Like Terms

Combining like terms involves grouping together terms that have the same variable raised to the same power. This helps simplify the equation. In the problem, the terms with the variable 'a' were on different sides. By adding 'a' to both sides, we combined these like terms. Initially, we had:

On the left side:
$4a$
On the right side:
$-a$

To combine, we performed the operation: \[4a + a = 5a\] This step is crucial because it reduces the number of terms and makes the equation simpler to work with.

Isolating the Variable

Isolating the variable means getting the variable alone on one side of the equation. This is done so we can solve for it. Once we combined the like terms, our equation was:
\[5a + 5 = -40\] To isolate 'a', we needed to remove the constant term (5). We did this by subtracting 5 from both sides:

Left side:
\[5a + 5 - 5 = 5a\]
Right side:
\[-40 - 5 = -45\]

This process simplified the equation to: \[5a = -45\]

Simplifying Equations

Simplifying an equation involves performing operations to make the equation as simple as possible, often reducing it to a single variable term. In our problem, once we isolated the variable term, we had:
\[5a = -45\] To solve for 'a', we divided both sides by 5:

Left side: \[\frac{5a}{5} = a\]
Right side: \[\frac{-45}{5} = -9\]

Thus, we found:
\[a = -9\]
This final simplification gives us the value of 'a'. Each step of combining, isolating, and simplifying helps make the original equation manageable and solvable.

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91影视

Solve the equations for the variable. $$4 a+5=-a-40$$

Short Answer

Step by step solution

Combine like terms

Isolate the variable term

Solve for the variable

Key Concepts

Combining Like Terms

Isolating the Variable

Simplifying Equations

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