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

-7|-5t-3|=1
Divide each term by -7 and simplify.
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
Solve the first equation for t.
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
Solve the second equation for t.
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

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