Question

Solve and check each equation. $$4 x-11=7 x+20$$

   Solve and check each equation.
$$4 x-11=7 x+20$$

Essentials of Precalculus

Essentials of Precalculus

Richard N. Aufmann,… 1st Edition

Chapter 1, Problem 4

Instant Answer

Solved by Expert Julie Silva

07/09/2021

Step 1

This gives us: \[4x - 7x - 11 = 7x - 7x + 20\] which simplifies to: \[-3x - 11 = 20\] Show more…

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Solve and check each equation. $$4 x-11=7 x+20$$

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Key Concepts

Linear Equations

Linear equations are algebraic expressions that represent straight lines when graphed. In these equations, the variable is only raised to the first power. Solving them involves finding the values of the variable that make the equation true by performing operations that maintain the equality.

Isolating the Variable

Isolating the variable means manipulating the equation using addition, subtraction, multiplication, or division to have the variable on one side of the equation and the constants on the other. This step-by-step approach simplifies the process of finding the solution.

Algebraic Manipulation

Algebraic manipulation is the process of rearranging and simplifying equations through the use of arithmetic operations and properties of equality. This includes combining like terms, moving terms from one side of the equation to the other, and simplifying expressions while preserving the equality.

Verification of the Solution

Verification of the solution involves substituting the found value back into the original equation to check if both sides of the equation are equal. This step is crucial to confirm that the solution is correct and that no errors were made during the manipulation steps.

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