Absolute value: Solve absolute value equations with a number outside the absolute value bars

Examples with solutions for Absolute value: Solve absolute value equations with a number outside the absolute value bars

Exercise #1

15= -\left|15\right| =

Step-by-Step Solution

To solve the given expression 15 -\left|15\right| , we need to find the absolute value of 15 15 , then apply the negative sign.

The absolute value of a number is the non-negative value of that number without regard to its sign.

Thus, 15=15 \left|15\right| = 15 .

Now apply the negative sign: 15=15 -\left|15\right| = -15 .

Therefore, the answer is 15 -15 .

Answer

15 -15

Exercise #2

7= -\left|7\right| =

Step-by-Step Solution

In the given expression, 7 -\left|7\right| , the absolute value of 7 7 is required.

The absolute value, 7 \left|7\right| , is 7 7 since absolute value denotes a non-negative distance from zero.

Applying the negative sign changes it to 7 -7 .

The final result, therefore, is 7 -7 .

Answer

7 -7

Exercise #3

23= -\left|23\right| =

Step-by-Step Solution

To solve the expression 23 -\left|23\right| , first find the absolute value of 23 23 .

The absolute value of a number is the distance between the number and zero on the number line, so 23=23 \left|23\right| = 23 .

Then apply the negative sign: 23=23 -\left|23\right| = -23 .

Hence, the correct answer is 23 -23 .

Answer

23 -23

Exercise #4

53= -\lvert5^3\rvert=

Step-by-Step Solution

First, calculate the cube of 5: 53=125 5^3 = 125 .

Then, apply the absolute value:
since 125 is positive, 125=125 \lvert 125 \rvert = 125 .

Finally, apply the negative sign outside the absolute value: 125=125 -\lvert 125 \rvert = -125 .

Answer

125 -125

Exercise #5

34= -\lvert3^4\rvert=

Step-by-Step Solution

First, calculate the fourth power of 3: 34=81 3^4 = 81 .

Then, apply the absolute value:
since 81 is positive, 81=81 \lvert 81 \rvert = 81 .

Finally, apply the negative sign outside the absolute value: 81=81 -\lvert 81 \rvert = -81 .

Answer

81 -81

Exercise #6

x3= -\left|-x^3\right|=

Step-by-Step Solution

The expression has an absolute value and a negative sign outside of the absolute value. When you take the absolute value of x3 -x^3 , it results in x3 |x^3| , which is x3 x^3 assumingx x is a real number. The negative sign outside the absolute value inverts it back to x3 -x^3 . Thus, the correct interpretation of the original expression x3 -\left|-x^3\right| is x3 -x^3 .

Answer

x3 -x^3

Exercise #7

2z= -\left|2z\right|=

Step-by-Step Solution

The absolute value function 2z \left|2z\right| simply returns 2z 2z when z z is positive and 2z -2z whenz z is negative, ensuring the result is non-negative. However, the minus sign outside the absolute value 2z -\left|2z\right| negates the result of the absolute value. Therefore, 2z -\left|2z\right| results in 2z -2z for all z z . Hence, the original expression evaluates to 2z -2z .

Answer

2z -2z

Exercise #8

3y2= -\left|3y^2\right|=

Step-by-Step Solution

The absolute value of 3y2 3y^2 is 3y2 3y^2 itself because 3y2 3y^2 is always non-negative regardless of the value of y y since any real number squared is non-negative. The negative sign outside the absolute value indicates that the expression3y2 -\left|3y^2\right| evaluates to 3y2 -3y^2 .

Answer

3y2 -3y^2

Exercise #9

y2= -\left|-y^2\right|=

Video Solution

Answer

y2 -y^2

Exercise #10

42= -\lvert4^2\rvert=

Video Solution

Answer

16 -16

Exercise #11

18= −\left|-18\right|=

Video Solution

Answer

18 -18