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Solve the following problem. Give the equation using [tex]$x$[/tex] as the variable, and provide the answer.

If 5 is added to eight times a number, the result is equal to 9 more than seven times the number. Find the number.

Write the equation using [tex]$x$[/tex] as the variable. Choose the correct equation below.

A. [tex]\( 5(8x) = 7x + 9 \)[/tex]

B. [tex]\( 8x + 5 = 9(7x) \)[/tex]

C. [tex]\( 8(x + 5) = 7(x + 9) \)[/tex]

D. [tex]\( 5(8x) = 9(7x) \)[/tex]

E. [tex]\( 8x + 5 = 7x + 9 \)[/tex]



Answer :

GinnyAnswer
Let's solve the given problem step by step.

Problem Statement:
If 5 is added to eight times a number, the result is equal to 9 more than seven times the number. Find the number.

Identify the Variable:
Let the number be [tex]\( x \)[/tex].

Construct the Equation:
The problem states that if 5 is added to eight times the number ([tex]\( 8x \)[/tex]), the result is equal to 9 more than seven times the number ([tex]\( 7x \)[/tex]). We can translate this problem into an equation.

So, the equation becomes:
[tex]\[ 8x + 5 = 7x + 9 \][/tex]

Among the given choices, the correct equation is:
E. [tex]\( 8x + 5 = 7x + 9 \)[/tex]

Solve the Equation:
To find the value of [tex]\( x \)[/tex], solve the equation step by step:

1. Start with the equation:
[tex]\[ 8x + 5 = 7x + 9 \][/tex]

2. Subtract [tex]\( 7x \)[/tex] from both sides to isolate terms involving [tex]\( x \)[/tex] on one side:
[tex]\[ 8x - 7x + 5 = 9 \][/tex]
[tex]\[ x + 5 = 9 \][/tex]

3. Subtract 5 from both sides to isolate [tex]\( x \)[/tex]:
[tex]\[ x + 5 - 5 = 9 - 5 \][/tex]
[tex]\[ x = 4 \][/tex]

Conclusion:
The number [tex]\( x \)[/tex] is [tex]\( 4 \)[/tex].

So, the equation representing the problem is [tex]\( 8x + 5 = 7x + 9 \)[/tex] and the solution to the equation is [tex]\( x = 4 \)[/tex].

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