QuestionSolve the equation: $\frac{3 x+23}{7}+\frac{x+36}{5}=13$ . Provide an integer or simplified fraction as the solution.

Studdy Solution

STEP 1

Assumptions1. The equation is $\frac{3 x+23}{7}+\frac{x+36}{5}=13$ . The solution set is a set of real numbers

STEP 2

To simplify the equation, we first need to find a common denominator for the fractions. The least common multiple of7 and5 is35.

STEP 3

Multiply each term by35 to get rid of the denominators.
$35 \cdot \frac{3 x+23}{7}+35 \cdot \frac{x+36}{5}=35 \cdot13$

STEP 4

implify each term.
$(3x+23) +7(x+36) =35 \cdot13$

STEP 5

istribute the5 and7 in each term.
$15x +115 +7x +252 =455$

STEP 6

Combine like terms.
$22x +367 =455$

STEP 7

Subtract367 from both sides to isolate the variable term.
$22x =455 -367$

STEP 8

Calculate the right side.
$22x =88$

STEP 9

Divide both sides by22 to solve for x.
$x = \frac{88}{22}$

STEP 10

Calculate the value of x.
$x =4$ The solution set is {4}.

Was this helpful?

QuestionSolve the equation: $\frac{3 x+23}{7}+\frac{x+36}{5}=13$ . Provide an integer or simplified fraction as the solution.

Studdy Solution

STEP 1

Assumptions1. The equation is $\frac{3 x+23}{7}+\frac{x+36}{5}=13$ . The solution set is a set of real numbers

STEP 2

To simplify the equation, we first need to find a common denominator for the fractions. The least common multiple of7 and5 is35.

STEP 3

Multiply each term by35 to get rid of the denominators.
$35 \cdot \frac{3 x+23}{7}+35 \cdot \frac{x+36}{5}=35 \cdot13$

STEP 4

implify each term.
$(3x+23) +7(x+36) =35 \cdot13$

STEP 5

istribute the5 and7 in each term.
$15x +115 +7x +252 =455$

STEP 6

Combine like terms.
$22x +367 =455$

STEP 7

Subtract367 from both sides to isolate the variable term.
$22x =455 -367$

STEP 8

Calculate the right side.
$22x =88$

STEP 9

Divide both sides by22 to solve for x.
$x = \frac{88}{22}$

STEP 10

Calculate the value of x.
$x =4$ The solution set is {4}.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSolve the equation: 3x+237+x+365=13\frac{3 x+23}{7}+\frac{x+36}{5}=1373x+23​+5x+36​=13. Provide an integer or simplified fraction as the solution.

Studdy Solution

STEP 1

Assumptions1. The equation is 3x+237+x+365=13\frac{3 x+23}{7}+\frac{x+36}{5}=1373x+23​+5x+36​=13 . The solution set is a set of real numbers

STEP 2

To simplify the equation, we first need to find a common denominator for the fractions. The least common multiple of7 and5 is35.

STEP 3

Multiply each term by35 to get rid of the denominators.35⋅3x+237+35⋅x+365=35⋅1335 \cdot \frac{3 x+23}{7}+35 \cdot \frac{x+36}{5}=35 \cdot1335⋅73x+23​+35⋅5x+36​=35⋅13

STEP 4

implify each term.(3x+23)+7(x+36)=35⋅13(3x+23) +7(x+36) =35 \cdot13(3x+23)+7(x+36)=35⋅13

STEP 5

istribute the5 and7 in each term.15x+115+7x+252=45515x +115 +7x +252 =45515x+115+7x+252=455

STEP 6

Combine like terms.22x+367=45522x +367 =45522x+367=455

STEP 7

Subtract367 from both sides to isolate the variable term.22x=455−36722x =455 -36722x=455−367

STEP 8

Calculate the right side.22x=8822x =8822x=88

STEP 9

Divide both sides by22 to solve for x.x=8822x = \frac{88}{22}x=2288​

STEP 10

Calculate the value of x.x=4x =4x=4The solution set is {4}.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSolve the equation: $\frac{3 x+23}{7}+\frac{x+36}{5}=13$ . Provide an integer or simplified fraction as the solution.

Assumptions1. The equation is $\frac{3 x+23}{7}+\frac{x+36}{5}=13$ . The solution set is a set of real numbers

Multiply each term by35 to get rid of the denominators.
$35 \cdot \frac{3 x+23}{7}+35 \cdot \frac{x+36}{5}=35 \cdot13$

implify each term.
$(3x+23) +7(x+36) =35 \cdot13$

istribute the5 and7 in each term.
$15x +115 +7x +252 =455$

Combine like terms.
$22x +367 =455$

Subtract367 from both sides to isolate the variable term.
$22x =455 -367$

Calculate the right side.
$22x =88$

Divide both sides by22 to solve for x.
$x = \frac{88}{22}$

Calculate the value of x.
$x =4$ The solution set is {4}.