Solved on Dec 10, 2023

Solve the equation $4x + 9 = 33$ and check the solutions $x = 7$ and $x = 6$ using substitution.

STEP 1

Assumptions
1. The equation to solve is $4x + 9 = 33$ .
2. Jesse's proposed solution is $x = 7$ .
3. Arron's proposed solution is $x = 6$ .
4. To check their answers, substitution of their proposed solutions into the original equation is required.

STEP 2

Explain the process of substitution to check an answer.
To check if a proposed solution for an equation is correct, we substitute the value of $x$ back into the original equation. If the left-hand side (LHS) of the equation equals the right-hand side (RHS) after substitution, then the proposed solution is correct. If not, the solution is incorrect.

STEP 3

First, we will check Jesse's answer by substituting $x = 7$ into the original equation.
$4x + 9 = 33$

STEP 4

Substitute $x = 7$ into the equation.
$4(7) + 9 = 33$

STEP 5

Perform the multiplication.
$28 + 9 = 33$

STEP 6

Add the numbers to see if the LHS equals the RHS.
$37 = 33$

STEP 7

Since $37 \neq 33$ , Jesse's answer of $x = 7$ is incorrect.

STEP 8

Now, we will check Arron's answer by substituting $x = 6$ into the original equation.
$4x + 9 = 33$

STEP 9

Substitute $x = 6$ into the equation.
$4(6) + 9 = 33$

STEP 10

Perform the multiplication.
$24 + 9 = 33$

STEP 11

Add the numbers to see if the LHS equals the RHS.
$33 = 33$

STEP 12

Since $33 = 33$ , Arron's answer of $x = 6$ is correct.
a) Jesse and Arron could use substitution to check their answers by replacing $x$ with their respective solutions in the original equation $4x + 9 = 33$ and verifying if the equation holds true.
b) Arron's answer is correct, as substituting $x = 6$ into the original equation results in both sides being equal. Jesse's answer is incorrect, as substituting $x = 7$ does not satisfy the equation.

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Solve the equation $4x + 9 = 33$ and check the solutions $x = 7$ and $x = 6$ using substitution.

STEP 1

Assumptions
1. The equation to solve is $4x + 9 = 33$ .
2. Jesse's proposed solution is $x = 7$ .
3. Arron's proposed solution is $x = 6$ .
4. To check their answers, substitution of their proposed solutions into the original equation is required.

STEP 2

STEP 3

First, we will check Jesse's answer by substituting $x = 7$ into the original equation.
$4x + 9 = 33$

STEP 4

Substitute $x = 7$ into the equation.
$4(7) + 9 = 33$

STEP 5

Perform the multiplication.
$28 + 9 = 33$

STEP 6

Add the numbers to see if the LHS equals the RHS.
$37 = 33$

STEP 7

Since $37 \neq 33$ , Jesse's answer of $x = 7$ is incorrect.

STEP 8

Now, we will check Arron's answer by substituting $x = 6$ into the original equation.
$4x + 9 = 33$

STEP 9

Substitute $x = 6$ into the equation.
$4(6) + 9 = 33$

STEP 10

Perform the multiplication.
$24 + 9 = 33$

STEP 11

Add the numbers to see if the LHS equals the RHS.
$33 = 33$

STEP 12

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Solve the equation 4x+9=334x + 9 = 334x+9=33 and check the solutions x=7x = 7x=7 and x=6x = 6x=6 using substitution.

STEP 1

Assumptions1. The equation to solve is 4x+9=334x + 9 = 334x+9=33.2. Jesse's proposed solution is x=7x = 7x=7.3. Arron's proposed solution is x=6x = 6x=6.4. To check their answers, substitution of their proposed solutions into the original equation is required.

STEP 2

STEP 3

First, we will check Jesse's answer by substituting x=7x = 7x=7 into the original equation.4x+9=334x + 9 = 334x+9=33

STEP 4

Substitute x=7x = 7x=7 into the equation.4(7)+9=334(7) + 9 = 334(7)+9=33

STEP 5

Perform the multiplication.28+9=3328 + 9 = 3328+9=33

STEP 6

Add the numbers to see if the LHS equals the RHS.37=3337 = 3337=33

STEP 7

Since 37≠3337 \neq 3337=33, Jesse's answer of x=7x = 7x=7 is incorrect.

STEP 8

Now, we will check Arron's answer by substituting x=6x = 6x=6 into the original equation.4x+9=334x + 9 = 334x+9=33

STEP 9

Substitute x=6x = 6x=6 into the equation.4(6)+9=334(6) + 9 = 334(6)+9=33

STEP 10

Perform the multiplication.24+9=3324 + 9 = 3324+9=33

STEP 11

Add the numbers to see if the LHS equals the RHS.33=3333 = 3333=33

STEP 12

Start learning now

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

Solve the equation $4x + 9 = 33$ and check the solutions $x = 7$ and $x = 6$ using substitution.

Assumptions
1. The equation to solve is $4x + 9 = 33$ .
2. Jesse's proposed solution is $x = 7$ .
3. Arron's proposed solution is $x = 6$ .
4. To check their answers, substitution of their proposed solutions into the original equation is required.

First, we will check Jesse's answer by substituting $x = 7$ into the original equation.
$4x + 9 = 33$

Substitute $x = 7$ into the equation.
$4(7) + 9 = 33$

Perform the multiplication.
$28 + 9 = 33$

Add the numbers to see if the LHS equals the RHS.
$37 = 33$

Since $37 \neq 33$ , Jesse's answer of $x = 7$ is incorrect.

Now, we will check Arron's answer by substituting $x = 6$ into the original equation.
$4x + 9 = 33$

Substitute $x = 6$ into the equation.
$4(6) + 9 = 33$

Perform the multiplication.
$24 + 9 = 33$

Add the numbers to see if the LHS equals the RHS.
$33 = 33$