Question

solve the equation $7x + 4 = 9$ algebraically. answer as a reduced fraction only.
$x = \square$

solve the equation $-4x - 5 = -9x + 11$ algebraically. answer as a reduced fraction only.
$x = \square$

solve the equation $8\left(-3x - 10\
ight) + 2 = -6\left(x - 11\
ight) + 11$ algebraically. answer as a reduced fraction only.
$x = \square$

question help: \boxed{\text{video 1}} \boxed{\text{video 2}} \boxed{\text{video 3}} \boxed{\text{video 4}} \boxed{\text{video 5}}

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Explanation:

Step1: Isolate term with $x$

Subtract 4 from both sides:
$7x + 4 - 4 = 9 - 4$
$7x = 5$

Step2: Solve for $x$

Divide both sides by 7:
$x = \frac{5}{7}$

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Step1: Collect $x$ terms on left

Add $9x$ to both sides:
$-4x + 9x - 5 = -9x + 9x + 11$
$5x - 5 = 11$

Step2: Isolate term with $x$

Add 5 to both sides:
$5x - 5 + 5 = 11 + 5$
$5x = 16$

Step3: Solve for $x$

Divide both sides by 5:
$x = \frac{16}{5}$

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Step1: Expand both sides

Apply distributive property:
$8(-3x) + 8(-10) + 2 = -6(x) + (-6)(-11) + 11$
$-24x - 80 + 2 = -6x + 66 + 11$

Step2: Simplify both sides

Combine constant terms:
$-24x - 78 = -6x + 77$

Step3: Collect $x$ terms on left

Add $6x$ to both sides:
$-24x + 6x - 78 = -6x + 6x + 77$
$-18x - 78 = 77$

Step4: Isolate term with $x$

Add 78 to both sides:
$-18x - 78 + 78 = 77 + 78$
$-18x = 155$

Step5: Solve for $x$

Divide both sides by $-18$:
$x = -\frac{155}{18}$

Answer:

$x = \frac{5}{7}$
$x = \frac{16}{5}$
$x = -\frac{155}{18}$