Solving Equations With Absolute Values Math

For most absolute value equations you will write two different equations to solve. Means these are the same. The absolute value of a times the absolute value of b which can also be useful when solving.

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The value inside of the absolute value can be positive or negative.

Solving equations with absolute values math. The absolute value of a times b and. When we attempt to solve the absolute value equation x 3 we are in effect setting two line equations equal to each other and finding where they cross. If the number is negative then the absolute value is its opposite. 4 the equation x k with k 0 has no real solutions.

The rules you need to know in order to be able to solve the question in this tutorial. Solve absolute value equations practice khan academy. High school math solutions quadratic equations calculator part 1. A b a b.

1 x 0 if x 0. If the answer to an absolute value equation is negative then the answer is the empty set. The general steps to solve an absolute value equation are. Then taking the square root will undo the squaring but leave it positive or zero.

Solve equations like 3 x 1 7 6 x 1 6. 5 the equation x k k 0 is equivalent to x k or x k. Rewrite the absolute value equation as two separate equations one positive and the other negative solve each equation separately after solving substitute your answers back into original equation to verify that you solutions are valid write. Solve equations like 3 x 1 7 6 x 1 6.

Review of absolute value. Set up two equations and solve them separately. 3 x x if x 0. If it s positive it s equal to the number.

It requires understanding of the absolute value property. Get the absolve value expression by itself. The challenge is that the absolute value of a number depends on the number s sign. If you re seeing this message it means we re having trouble loading external resources on our website.

In the above i ve plotted the graph of y 1 x being the blue line that looks like a v and y 2 3 being the green horizontal line. A quadratic equation is a second degree polynomial having the general form ax 2 bx c 0 where a b and c. Solving absolute value equations is somewhat tricky. U a is the same as u a and vice versa.

No absolute value can be a negative number. Absolute value equations are equations where the variable is within an absolute value operator like x 5 9. 2 x x if x 0. Solve an absolute value equation using the following steps.