QuestionSolve the equation using addition and multiplication principles:
$5[7-5(6-r)]-7=7[5(7 r-6)+4]-50$
What is the solution? A. $r=\square$ , B. all real numbers, C. no solution.

Studdy Solution

STEP 1

Assumptions1. The variable r is a real number. . We are to solve for r using the addition and multiplication principles.

STEP 2

First, we need to simplify the equation by distributing the multiplication across the terms inside the brackets.
$5[7-5(6-r)]-7=7[5(7 r-6)+4]-50$ becomes $5[7-30+5r]-7=7[35r-30+4]-50$

STEP 3

implify further by performing the operations inside the brackets.
$5[-23+5r]-7=7[35r-26]-50$ becomes $-115+25r-7=245r-182-50$

STEP 4

implify further by combining like terms on each side of the equation.
$-122+25r=245r-232$

STEP 5

Next, we use the addition principle to isolate the variable r on one side of the equation. We do this by subtracting25r from both sides of the equation.
$-122+25r-25r=245r-232-25r$ which simplifies to $-122=220r-232$

STEP 6

We then add232 to both sides of the equation to isolate the term with r on one side.
$-122+232=220r-232+232$ which simplifies to $110=220r$

STEP 7

Finally, we use the multiplication principle to solve for r by dividing both sides of the equation by220.
$\frac{110}{220}=\frac{220r}{220}$ which simplifies to $r=\frac{1}{2}$

STEP 8

To check our solution, we substitute r =1/2 back into the original equation and simplify to see if both sides of the equation are equal.
$5[7-5(6-\frac{1}{2})]-7=7[5(7 \times \frac{1}{2}-6)+4]-50$ which simplifies to $5[7-5 \times \frac{11}{2}]-7=7[5 \times \frac{7}{2}-30+4]-50$ which simplifies further to $5[-\frac{3}{2}]-7=7[\frac{7}{2}-26]-50$ which simplifies to $-\frac{15}{2}-7=-\frac{63}{2}-50$ which simplifies to $-\frac{29}{2}=-\frac{113}{2}$ Since both sides of the equation are not equal, there is no solution for the given equation.
So the correct choice is C. There is no solution.

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QuestionSolve the equation using addition and multiplication principles:
$5[7-5(6-r)]-7=7[5(7 r-6)+4]-50$
What is the solution? A. $r=\square$ , B. all real numbers, C. no solution.

Studdy Solution

STEP 1

Assumptions1. The variable r is a real number. . We are to solve for r using the addition and multiplication principles.

STEP 2

First, we need to simplify the equation by distributing the multiplication across the terms inside the brackets.
$5[7-5(6-r)]-7=7[5(7 r-6)+4]-50$ becomes $5[7-30+5r]-7=7[35r-30+4]-50$

STEP 3

implify further by performing the operations inside the brackets.
$5[-23+5r]-7=7[35r-26]-50$ becomes $-115+25r-7=245r-182-50$

STEP 4

implify further by combining like terms on each side of the equation.
$-122+25r=245r-232$

STEP 5

Next, we use the addition principle to isolate the variable r on one side of the equation. We do this by subtracting25r from both sides of the equation.
$-122+25r-25r=245r-232-25r$ which simplifies to $-122=220r-232$

STEP 6

We then add232 to both sides of the equation to isolate the term with r on one side.
$-122+232=220r-232+232$ which simplifies to $110=220r$

STEP 7

Finally, we use the multiplication principle to solve for r by dividing both sides of the equation by220.
$\frac{110}{220}=\frac{220r}{220}$ which simplifies to $r=\frac{1}{2}$

STEP 8

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QuestionSolve the equation using addition and multiplication principles: 5[7−5(6−r)]−7=7[5(7r−6)+4]−50 5[7-5(6-r)]-7=7[5(7 r-6)+4]-50 5[7−5(6−r)]−7=7[5(7r−6)+4]−50 What is the solution? A. r=□r=\squarer=□, B. all real numbers, C. no solution.

Studdy Solution

STEP 1

Assumptions1. The variable r is a real number. . We are to solve for r using the addition and multiplication principles.

STEP 2

STEP 3

implify further by performing the operations inside the brackets.5[−23+5r]−7=7[35r−26]−505[-23+5r]-7=7[35r-26]-505[−23+5r]−7=7[35r−26]−50becomes−115+25r−7=245r−182−50-115+25r-7=245r-182-50−115+25r−7=245r−182−50

STEP 4

implify further by combining like terms on each side of the equation.−122+25r=245r−232-122+25r=245r-232−122+25r=245r−232

STEP 5

STEP 6

We then add232 to both sides of the equation to isolate the term with r on one side.−122+232=220r−232+232-122+232=220r-232+232−122+232=220r−232+232which simplifies to110=220r110=220r110=220r

STEP 7

Finally, we use the multiplication principle to solve for r by dividing both sides of the equation by220.110220=220r220\frac{110}{220}=\frac{220r}{220}220110​=220220r​which simplifies tor=12r=\frac{1}{2}r=21​

STEP 8

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Studdy solves anything!

Start learning now

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QuestionSolve the equation using addition and multiplication principles:
$5[7-5(6-r)]-7=7[5(7 r-6)+4]-50$
What is the solution? A. $r=\square$ , B. all real numbers, C. no solution.

implify further by performing the operations inside the brackets.
$5[-23+5r]-7=7[35r-26]-50$ becomes $-115+25r-7=245r-182-50$

implify further by combining like terms on each side of the equation.
$-122+25r=245r-232$

We then add232 to both sides of the equation to isolate the term with r on one side.
$-122+232=220r-232+232$ which simplifies to $110=220r$

Finally, we use the multiplication principle to solve for r by dividing both sides of the equation by220.
$\frac{110}{220}=\frac{220r}{220}$ which simplifies to $r=\frac{1}{2}$