QuestionChoose the expressions equivalent to $(6 u-4)-(3 u-8)$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $(6 u-4)-(3 u-8)$ . We are looking for expressions that are equivalent to the given expression

STEP 2

First, we need to simplify the given expression. We can do this by distributing the negative sign in the second part of the expression.
$(6 u-4)-( u-8) =6u -4 -u +8$

STEP 3

Next, we combine like terms.
$6u - -3u +8 = (6u -3u) + (- +8)$

STEP 4

implify the expression.
$6u -3u =3u$ $-4 +8 =4$ So, the simplified expression is $3u +4$

STEP 5

Now, we need to check which of the provided expressions are equivalent to $3u +4$ .The first expression is $-3 u+4+ u$ . Simplify this expression by combining like terms.
$-3 u+4+ u = (-3u +u) +4 =3u +4$ So, the first expression is equivalent to the given expression.

STEP 6

The second expression is $(-4 u+6)-(3 u-8)$ . Simplify this expression by distributing the negative sign and combining like terms.
$(-4 u+6)-(3 u-8) = -4u +6 -3u +8 = (-4u -3u) + (6 +8) = -u +14$ So, the second expression is not equivalent to the given expression.

STEP 7

The third expression is $(6 u-4)-(- u+3)$ . Simplify this expression by distributing the negative sign and combining like terms.
$(6 u-4)-(- u+3) =6u -4 +u -3 = (6u +u) - (4 +3) =14u -7$ So, the third expression is not equivalent to the given expression.

STEP 8

The fourth expression is $(-4 u+6)-(-8 u+3)$ . Simplify this expression by distributing the negative sign and combining like terms.
$(-4 u+6)-(-8 u+3) = -4u +6 +8u -3 = (-4u +8u) + (6 -3) =4u +3$ So, the fourth expression is not equivalent to the given expression.
The expressions equivalent to $(6 u-4)-(3 u-8)$ are $-3 u+4+6 u$ .

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