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2 years ago

11

Simplify the expression

title="6(5 + t) - 3(t + 3)" alt="6(5 + t) - 3(t + 3)" align="absmiddle" class="latex-formula">

1 answer:

Pavel [41]2 years ago

3 0

30+6t - 3t-9
combine 6t and -3t and get 3t
30+3t=-9
subtract 30 on both sides
3t=-39
divide by 3
t=13

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$a. $ x = -2\\b. $ x = \frac{3}{2} \\c. $ x = 0\\d. $ x = -\frac{1}{5}$

Each of the equations can be solved as shown below:

a. $3x + 7 = - x - 1$

$3x + 7 + x = - x - 1 + x$ (<em>addition property of equality</em>)

$4x + 7 = - 1\\4x + 7 - 7 = -1-7$ (<em>Subtraction property of equality</em>)

$4x = -8\\\frac{4x}{4} = \frac{-8}{4}$ <em> (Division property of equality)</em>

<em /> $x = -2$

b. $1 - 2x + 5 = 4x - 3\\$

<em>Add like terms </em>

<em /> $6 - 2x = 4x - 3\\\\6 - 2x - 6 = 4x - 3 - 6$ (<em>Subtraction property of equality</em>)

$- 2x = 4x - 9\\-2x - 4x = 4x -9 - 4x$ <em> (Subtraction property of equality)</em>

<em /> $-6x = -9 \\\frac{-6x}{-6} = \frac{-9}{-6}$ <em> (Division property of equality)</em>

<em /> $x = \frac{3}{2}$

c. $4x - 2 + x =-2 + 2x\\$

$5x - 2 = -2 + 2x\\5x - 2x = -2 + 2\\3x = 0\\ x = \frac{0}{3} \\x = 0$

d. $3x - 4 + 1 = - 2x -5 + 5x\\$

$3x - 3 = - 7x -5\\3x + 7x = 3 - 5\\10x = -2\\x = \frac{-2}{10} \\x = -\frac{1}{5}$

<em>The value of x in each </em><em>equation</em><em> are:</em>

<em /> $a. $ x = -2\\b. $ x = \frac{3}{2} \\c. $ x = 0\\d. $ x = -\frac{1}{5}$

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