-7|-5t-3|=1

Divide each term in -7|-5t-3|=1 by -7.

-7|-5t-3|-7=1-7

Cancel the common factor of -7.

Cancel the common factor.

-7|-5t-3|-7=1-7

Divide |-5t-3| by 1.

|-5t-3|=1-7

|-5t-3|=1-7

Move the negative in front of the fraction.

|-5t-3|=-17

|-5t-3|=-17

Remove the absolute value term. This creates a ± on the right side of the equation because |x|=±x.

-5t-3=±(-17)

Set up the positive portion of the ± solution.

-5t-3=-17

Move all terms not containing t to the right side of the equation.

Add 3 to both sides of the equation.

-5t=-17+3

To write 3 as a fraction with a common denominator, multiply by 77.

-5t=-17+3⋅77

Combine 3 and 77.

-5t=-17+3⋅77

Combine the numerators over the common denominator.

-5t=-1+3⋅77

Simplify the numerator.

Multiply 3 by 7.

-5t=-1+217

Add -1 and 21.

-5t=207

-5t=207

-5t=207

Divide each term by -5 and simplify.

Divide each term in -5t=207 by -5.

-5t-5=207⋅(-15)

Cancel the common factor of -5.

Cancel the common factor.

-5t-5=207⋅(-15)

Divide t by 1.

t=207⋅(-15)

t=207⋅(-15)

Simplify 207⋅(-15).

Cancel the common factor of 5.

Move the leading negative in -15 into the numerator.

t=207⋅-15

Factor 5 out of 20.

t=5(4)7⋅-15

Cancel the common factor.

t=5⋅47⋅-15

Rewrite the expression.

t=47⋅-1

t=47⋅-1

Combine 47 and -1.

t=4⋅-17

Simplify the expression.

Multiply 4 by -1.

t=-47

Move the negative in front of the fraction.

t=-47

t=-47

t=-47

t=-47

t=-47

Set up the negative portion of the ± solution.

-5t-3=17

Move all terms not containing t to the right side of the equation.

Add 3 to both sides of the equation.

-5t=17+3

To write 3 as a fraction with a common denominator, multiply by 77.

-5t=17+3⋅77

Combine 3 and 77.

-5t=17+3⋅77

Combine the numerators over the common denominator.

-5t=1+3⋅77

Simplify the numerator.

Multiply 3 by 7.

-5t=1+217

Add 1 and 21.

-5t=227

-5t=227

-5t=227

Divide each term by -5 and simplify.

Divide each term in -5t=227 by -5.

-5t-5=227⋅(-15)

Cancel the common factor of -5.

Cancel the common factor.

-5t-5=227⋅(-15)

Divide t by 1.

t=227⋅(-15)

t=227⋅(-15)

Multiply 227(-15).

Multiply 227 and 15.

t=-227⋅5

Multiply 7 by 5.

t=-2235

t=-2235

t=-2235

t=-2235

The solution to the equation includes both the positive and negative portions of the solution.

t=-47,-2235

Exclude the solutions that do not make -7|-5t-3|=1 true.

No solution

Solve for t -7|-5t-3|=1