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Use the properties of operations to simplify the following algebraic expression. Rewrite the expression by following the directions in each step:

[tex]\[ 5(x - 4) + 3x - 9x + 7 \][/tex]

Step 1: Rewrite the subtraction operations as addition of negative numbers.

Step 2: Use the distributive property.

Sagot :

GinnyAnsweridn
Sure! Let's simplify the given algebraic expression step by step:

[tex]\[ 5(x-4) + 3x - 9x + 7 \][/tex]

### Step 1: Rewrite the subtraction operations as additions of negative numbers.

Rewrite each subtraction as an addition with a negative:
[tex]\[ 5(x + (-4)) + 3x + (-9)x + 7 \][/tex]

### Step 2: Use the distributive property.

Use the distributive property to remove parentheses:
[tex]\[ 5(x + (-4)) = 5 \cdot x + 5 \cdot (-4) \][/tex]
[tex]\[ = 5x + (-20) \][/tex]

So, the expression now becomes:
[tex]\[ 5x + (-20) + 3x + (-9)x + 7 \][/tex]

### Combine like terms.

Combine the terms with [tex]\( x \)[/tex]:

[tex]\[ 5x + 3x + (-9)x \][/tex]
[tex]\[ (5 + 3 - 9)x \][/tex]
[tex]\[ = (8 - 9)x \][/tex]
[tex]\[ = -1x \][/tex]

Now, combine the constant terms:

[tex]\[ -20 + 7 \][/tex]
[tex]\[ = -13 \][/tex]

### Final simplified expression.

Putting it all together, the simplified expression is:
[tex]\[ -1x - 13 \][/tex]

or more compactly:
[tex]\[ -x - 13 \][/tex]

So, the simplified algebraic expression is:
[tex]\[ -x - 13 \][/tex]

Answer:
[tex]\[ -x - 13 \][/tex]
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