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Simplify the expression [tex]\( 4(x + 3) - 5(x - 2) \)[/tex].

A. [tex]\(-x + 22\)[/tex]
B. [tex]\(-9x + 22\)[/tex]
C. [tex]\(x - 22\)[/tex]
D. [tex]\(-x - 22\)[/tex]

Sagot :

GinnyAnswer
To simplify the expression [tex]\(4(x+3)-5(x-2)\)[/tex], let's go through it step by step:

1. Distribute the constants inside the parentheses:

- Distribute the 4 in [tex]\(4(x + 3)\)[/tex]
[tex]\[ 4 \cdot x + 4 \cdot 3 = 4x + 12 \][/tex]
- Distribute the -5 in [tex]\(-5(x - 2)\)[/tex]
[tex]\[ -5 \cdot x - 5 \cdot (-2) = -5x + 10 \][/tex]

2. Combine the distributed parts:

Now we have:
[tex]\[ 4x + 12 - 5x + 10 \][/tex]

3. Group like terms:

- Combine the [tex]\(x\)[/tex] terms:
[tex]\[ 4x - 5x = -x \][/tex]
- Combine the constant terms:
[tex]\[ 12 + 10 = 22 \][/tex]

4. Write the simplified expression:

Putting it all together, we get:
[tex]\[ -x + 22 \][/tex]

So, the simplified expression is [tex]\(-x + 22\)[/tex].
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