How To Solve For X In An Absolute Value Equation

This is actually my first year ever teaching students to solve absolute value equations. Solve for x in the following equation.

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You begin by making it into two separate equations and then solving them separately.

How to solve for x in an absolute value equation. Now we know that p 0 p 0 and so cant ever be less than zero. 2x - 1 -3. The absolute value is already isolated.

Solve each equation separately. Its always easiest to understand a math concept by looking at. These answers may not be solutions to the equation.

X 7 2. X could be 15. This equation has no solution.

The absolute value of a number is its distance from 0 on the number line. To solve absolute value equations first isolate the absolute value terms by moving anything outside of the vertical bars to the other side of the equation. After solving substitute your answers back into original equation to verify that you solutions are valid.

Well leave it to you to verify that the first potential solution does in fact work and so there is a single solution to this equation. If the left side of the equation equals the right side of the equation after the. 2x - 1 3.

Absolute value of a number is the positive value of the number. Just as you would divide both sides of an equation by a coefficient that is being multiplied by x you would square both sides of an equation if x appears under the square root or the radical sign. Solve the equation 2x-15 Solve the equation 2x-1-5 The answers are 3 and -2.

The solutions are x 6 and x -3. Sign in with Facebook. To solve an equation such as 8 2 x 6 8 2 x 6 we notice that the absolute value will be equal to 8 if the quantity inside the absolute value is 8 or -8.

To solve an absolute value equation as. Now the second equation x 2 5 reads. About absolute value equations.

Either 2x-15 or 2x-1-5 Step 2. Simplify all the absolute values then solve normally. Set up two equations and solve them separately.

Article Summary X. Key Points to Remember when Solving Absolute Value Equations. X 7 14.

2 -3 3 -6 3 -9 9. Solve for x. As such its always non-negative.

Write two equations without absolute value bars. Isolate the absolute value expression. And notice both of these numbers are exactly 10 away from the number 5.

X when x is less than zero this flips the number back to positive So when a number is positive or zero we leave it alone when it is negative we change it to positive using x. Sign in with Office365. So that being said the absolute value of -78 is 78 because -78 is 78 places away from 0.

B x9 0 x 9 0 Show Solution. The absolute value of a number is never negative. For instance the absolute v.

Solve an absolute value equation using the following steps. It contains plenty of examples and practice problemsM. This math video tutorial explains how to solve absolute value equations with variables on both sides.

They werent included in Oklahomas old standards for Algebra 1. Your first equation x 2 5 reads. Write out the final solution or graph it as needed.

Learn how to solve absolute value equations with multiple steps. I made this new solving absolute value equations foldable for my Algebra 1 students to glue in their interactive notebooks. Distance can never be negative.

2 6 3 12 3 9 9. Furthermore a b is the distance from a to b. So our solution theres two xs that satisfy this equation.

2x - 1 -3. Now that we can graph an absolute value function we will learn how to solve an absolute value equation. 2x - 1 3.

X frac14 and notice that this is less than 2 as our assumption required and so is a solution to the equation with the absolute value in it. Is the number on the other side of the equation negative. Therefore the absolute value of a number is always positive.

Solve the positive version of the equation. Therefore in this case there is no solution since it is impossible for an absolute value to be strictly less than zero ie. For emphasis left x right to left x right.

The x inside the absolute value symbol left right could be any expressions. Which says the absolute value of x equals. A 3x 2 x 2 0 Show Solution.

Check the solution x3 by substituting 3 in the original equation for x. Get the absolve value expression by itself. Negative 5 minus 5 is negative 10.

X 7 14. 15 minus 5 is 10 take the absolute value youre going to get 10 or x could be negative 5. The sign of left x right must be positive.

Has two solutions x a and x -a because both numbers are at the distance a from 0. Isolate the absolute value 2x - 1 3 6 2x - 1 3. Take a look at the problem below for a concrete example of the steps.

The a on the right side of the equation must be either a positive number or zero to have a solution. Absolute value is indicated by the absolute value bars. Solve the negative version of the equation by multiplying the quantity on the other side of the equals sign by 1.

Once you know this the rest is easy. For absolute value remember that the simplified version of the absolute value of a number will always be positive because absolute value means the distance from 0. Rewrite the absolute value equation as two separate equations one positive and the other negative.

0 when x equals 0. X a. Take the absolute value you get 10.

No its a positive number 3 so continue on to step 3. The distance from x to 2 equals 5 hence x 3 or x 7. The general steps for solving an absolute value equation are.

X when x is greater than zero. The General Steps to solve an absolute value equation are. Whats called absolute value of a number is just the numberss distance from zero.

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