Chloemadison245idn
Answered

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How many solutions are there to the equation below?

[tex]\[ 6x + 35 + 9x = 15(x + 4) - 25 \][/tex]

A. 1
B. Infinitely many
C. 0

Sagot :

GinnyAnsweridn
To determine the number of solutions to the equation

[tex]\[ 6x + 35 + 9x = 15(x + 4) - 25, \][/tex]

we'll follow the step-by-step process of simplifying and analyzing the equation.

### Step 1: Simplify both sides of the equation
First, combine like terms on each side of the equation starting with the left-hand side:

[tex]\[ 6x + 9x + 35 = 15x \][/tex]

This simplifies to:

[tex]\[ 15x + 35 \][/tex]

Next, expand on the right-hand side:

[tex]\[ 15(x + 4) - 25 \][/tex]
[tex]\[ 15x + 60 - 25 \][/tex]

Simplify the right-hand side:

[tex]\[ 15x + 35 \][/tex]

### Step 2: Set the simplified forms equal to each other
Now we equate the simplified left-hand side to the simplified right-hand side:

[tex]\[ 15x + 35 = 15x + 35 \][/tex]

### Step 3: Analyze the resulting equation
Notice that the equation:

[tex]\[ 15x + 35 = 15x + 35 \][/tex]

is true for all values of [tex]\( x \)[/tex]. This means that no matter what value [tex]\( x \)[/tex] takes, the equation will always hold true.

### Step 4: Conclusion
Since the equation is valid for all values of [tex]\( x \)[/tex], there are infinitely many solutions.

The number of solutions to the equation is:

[tex]\[ \text{B. Infinitely many} \][/tex]
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