QuestionSolve for $q$ : $-5(3-q)+4=5q-11$ .

Studdy Solution

STEP 1

Assumptions1. The equation is $-5(3-q)+4=5 q-11$ . We are solving for the variable $q$

STEP 2

First, distribute the $-5$ on the left side of the equation.
$-5(-q)+4 = -15+5q+4$

STEP 3

implify the left side of the equation.
$-15+5q+ = -11+5q$

STEP 4

Now, simplify the right side of the equation.
$q-11$

STEP 5

Set the simplified left side of the equation equal to the simplified right side of the equation.
$-11+5q =5q-11$

STEP 6

Subtract $5q$ from both sides of the equation to isolate $q$ on one side.
$-11 = -11$

STEP 7

The equation $-11 = -11$ is true for all values of $q$ . Therefore, the original equation $-5(3-q)+4=5 q-11$ has infinitely many solutions.
So, the solution is $q$ is any real number.

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QuestionSolve for $q$ : $-5(3-q)+4=5q-11$ .

Studdy Solution

STEP 1

Assumptions1. The equation is $-5(3-q)+4=5 q-11$ . We are solving for the variable $q$

STEP 2

First, distribute the $-5$ on the left side of the equation.
$-5(-q)+4 = -15+5q+4$

STEP 3

implify the left side of the equation.
$-15+5q+ = -11+5q$

STEP 4

Now, simplify the right side of the equation.
$q-11$

STEP 5

Set the simplified left side of the equation equal to the simplified right side of the equation.
$-11+5q =5q-11$

STEP 6

Subtract $5q$ from both sides of the equation to isolate $q$ on one side.
$-11 = -11$

STEP 7

The equation $-11 = -11$ is true for all values of $q$ . Therefore, the original equation $-5(3-q)+4=5 q-11$ has infinitely many solutions.
So, the solution is $q$ is any real number.

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QuestionSolve for qqq: −5(3−q)+4=5q−11-5(3-q)+4=5q-11−5(3−q)+4=5q−11.

Studdy Solution

STEP 1

Assumptions1. The equation is −5(3−q)+4=5q−11-5(3-q)+4=5 q-11−5(3−q)+4=5q−11 . We are solving for the variable qqq

STEP 2

First, distribute the −5-5−5 on the left side of the equation.−5(−q)+4=−15+5q+4-5(-q)+4 = -15+5q+4−5(−q)+4=−15+5q+4

STEP 3

implify the left side of the equation.−15+5q+=−11+5q-15+5q+ = -11+5q−15+5q+=−11+5q

STEP 4

Now, simplify the right side of the equation.q−11q-11q−11

STEP 5

Set the simplified left side of the equation equal to the simplified right side of the equation.−11+5q=5q−11-11+5q =5q-11−11+5q=5q−11

STEP 6

Subtract 5q5q5q from both sides of the equation to isolate qqq on one side.−11=−11-11 = -11−11=−11

STEP 7

The equation −11=−11-11 = -11−11=−11 is true for all values of qqq. Therefore, the original equation −5(3−q)+4=5q−11-5(3-q)+4=5 q-11−5(3−q)+4=5q−11 has infinitely many solutions.So, the solution is qqq is any real number.

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QuestionSolve for $q$ : $-5(3-q)+4=5q-11$ .

Assumptions1. The equation is $-5(3-q)+4=5 q-11$ . We are solving for the variable $q$

First, distribute the $-5$ on the left side of the equation.
$-5(-q)+4 = -15+5q+4$

implify the left side of the equation.
$-15+5q+ = -11+5q$

Now, simplify the right side of the equation.
$q-11$

Set the simplified left side of the equation equal to the simplified right side of the equation.
$-11+5q =5q-11$

Subtract $5q$ from both sides of the equation to isolate $q$ on one side.
$-11 = -11$

The equation $-11 = -11$ is true for all values of $q$ . Therefore, the original equation $-5(3-q)+4=5 q-11$ has infinitely many solutions.
So, the solution is $q$ is any real number.