*Solving linear equations in algebra is done with multiplication, division, or reciprocals.*

*Solving linear equations in algebra is done with multiplication, division, or reciprocals.*

In these equations, we will need to undo two operations in order to isolate the variable.

In each of the examples above, there was a single step to perform before we had our answer.

Solve: \(2x-7=13\) Notice the two operations happening to \(x\): it is being multiplied by 2 and then having 7 subtracted. But, only the \(x\) is being multiplied by 2, so the first step will be to add 7 to both sides. Adding 7 to both sides: \(\begin 2x-7 &= 13\\ 2x-7 \color & =13 \color\\ 2x&=20\end\) Now divide both sides by 2: \(\begin 2x &=20 \\ \dfrac&=\dfrac\\ x&= \boxed\end\) Just like with simpler problems, you can check your answer by substituting your value of \(x\) back into the original equation.

\(\begin2x-7&=13\\ 2(10) – 7 &= 13\\ 13 &= 13\end\) This is true, so we have the correct answer.

Solve: \(3x 2=4x-1\) Since both sides are simplified (there are no parentheses we need to figure out and no like terms to combine), the next step is to get all of the x’s on one side of the equation and all the numbers on the other side.

The same rule applies – whatever you do to one side of the equation, you must do to the other side as well!

It is possible to either move the \(3x\) or the \(4x\). Since it is positive, you would do this by subtracting it from both sides: \(\begin3x 2 &=4x-1\ 3x 2\color &=4x-1\color\ -x 2 & =-1\end\) Now the equation looks like those that were worked before.

The next step is to subtract 2 from both sides: \(\begin-x 2\color &= -1\color\-x=-3\end\) Finally, since \(-x= -1x\) (this is always true), divide both sides by \(-1\): \(\begin\dfrac &=\dfrac\ x&=3\end\) You should take a moment and verify that the following is a true statement: \(3(3) 2 = 4(3) – 1\) In the next example, we will need to use the distributive property before solving.

This isn’t 100% necessary for every problem, but it is a good habit so we will do it for our equations.

In this example, our original equation was \(4x = 8\).

## Comments Linear Equation Problem Solving

## SOLVING EQUATIONS - SOS Math

This sections illustrates the process of solving equations of various forms. It also shows. LINEAR EQUATIONS - Solve for x in the following equations. x - 4 = 10.…

## Word problems that lead to simple linear equations - Cut the Knot

Word problems that lead to simple linear equations Interpretation and solution of a. To be solved, a word problem must be translated into the language of.…

## Solving linear equations NZ Maths

Solve simple linear equations and interpret the answers in context. linear and quadratic problems in symbolic form and solved the problems by processes of.…

## Solving Simple Linear Equations - CliffsNotes

Algebraic equations are translated from complete English sentences. These equations can be solved. In fact, in order to successfully solve a word problem.…

## Problem Set - Solving Systems of Linear Equations

Solve the following system of equations by elimination. Answer x =.5; y = 1.67. Solution Rewrite in order to align the x and y terms. Add the second equation to.…

## Systems of Linear Equations and Word Problems – She Loves Math

Solving Systems with Linear. is to add or subtract the equations so that one.…

## Algebra - Linear Equations Practice Problems

Here is a set of practice problems to accompany the Linear Equations section of the Solving Equations and Inequalities chapter of the notes for Paul Dawkins Algebra course at Lamar University.…

## Linear equation word problems - Khan Academy

Watch Sal work through a basic Linear equations word problem. Solving linear equations and linear inequalities — Harder example. Linear equation word.…

## IXL - Solve linear equations word problems Algebra 1 practice

Improve your math knowledge with free questions in "Solve linear equations word problems" and thousands of other math skills.…

## Problem solving using Linear Equations -

Problem solving using Linear Equations. the passengers will have finished their linear equation word problems and look up in time to wave. where the problem describes a number in terms of.…