Math

QuestionFind the number of solutions for the equation: 20k1813=7(4k+15)-20 k-18-13=7(-4 k+15). Options: no solution, one solution, infinitely many solutions.

Studdy Solution

STEP 1

Assumptions1. The equation is 20k1813=7(4k+15)-20k -18 -13 =7(-4k +15). We are looking for the number of solutions this equation

STEP 2

First, simplify the left side of the equation.
20k1813=20k31-20k -18 -13 = -20k -31

STEP 3

Next, distribute the7 on the right side of the equation.
7(k+15)=28k+1057(-k +15) = -28k +105

STEP 4

Now, set the simplified left side of the equation equal to the simplified right side of the equation.
20k31=28k+105-20k -31 = -28k +105

STEP 5

Move the 28k-28k term from the right side to the left side by adding 28k28k to both sides.
20k+28k31=105-20k +28k -31 =105

STEP 6

implify the left side of the equation.
8k31=1058k -31 =105

STEP 7

Move the 31-31 term from the left side to the right side by adding 3131 to both sides.
k=105+31k =105 +31

STEP 8

implify the right side of the equation.
8k=1368k =136

STEP 9

Finally, solve for kk by dividing both sides by 88.
k=136/8k =136 /8

STEP 10

Calculate the value of kk.
k=17k =17The equation has one solution, k=17k =17.

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