Extra Practice: Solve the six algebraic equations provided.

Let's solve each equation step by step.

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1. $-6 + \frac{x}{4} = -5$

Step 1: Add 6 to both sides
$$
\frac{x}{4} = -5 + 6 = 1
$$

Step 2: Multiply both sides by 4
$$
x = 4 \times 1 = 4
$$

✔ Answer: $x = 4$

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2. $6 = \frac{a}{4} + 2$

Step 1: Subtract 2 from both sides
$$
6 - 2 = \frac{a}{4} \Rightarrow 4 = \frac{a}{4}
$$

Step 2: Multiply both sides by 4
$$
a = 4 \times 4 = 16
$$

✔ Answer: $a = 16$

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3. $-2 = 2 + \frac{v}{4}$

Step 1: Subtract 2 from both sides
$$
-2 - 2 = \frac{v}{4} \Rightarrow -4 = \frac{v}{4}
$$

Step 2: Multiply both sides by 4
$$
v = -4 \times 4 = -16
$$

✔ Answer: $v = -16$

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4. $\frac{6}{7} = \frac{4}{9} + v$

Step 1: Subtract $\frac{4}{9}$ from both sides
$$
v = \frac{6}{7} - \frac{4}{9}
$$

Step 2: Find common denominator (LCM of 7 and 9 is 63)
$$
\frac{6}{7} = \frac{54}{63},\quad \frac{4}{9} = \frac{28}{63}
$$
$$
v = \frac{54}{63} - \frac{28}{63} = \frac{26}{63}
$$

✔ Answer: $v = \frac{26}{63}$

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5. $\frac{1}{2} + \frac{2}{5}t - 1 = \frac{1}{5}t + t$

Step 1: Simplify both sides

Left side:
$$
\frac{1}{2} - 1 + \frac{2}{5}t = -\frac{1}{2} + \frac{2}{5}t
$$

Right side:
$$
\frac{1}{5}t + t = \frac{1}{5}t + \frac{5}{5}t = \frac{6}{5}t
$$

Now the equation is:
$$
-\frac{1}{2} + \frac{2}{5}t = \frac{6}{5}t
$$

Step 2: Subtract $\frac{2}{5}t$ from both sides
$$
-\frac{1}{2} = \frac{6}{5}t - \frac{2}{5}t = \frac{4}{5}t
$$

Step 3: Solve for $t$
$$
t = -\frac{1}{2} \div \frac{4}{5} = -\frac{1}{2} \times \frac{5}{4} = -\frac{5}{8}
$$

✔ Answer: $t = -\frac{5}{8}$

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6. $\frac{1}{5}m + \frac{2}{3} - 2 = m - \frac{2}{5}$

Step 1: Simplify constants on the left
$$
\frac{2}{3} - 2 = \frac{2}{3} - \frac{6}{3} = -\frac{4}{3}
$$

So the equation becomes:
$$
\frac{1}{5}m - \frac{4}{3} = m - \frac{2}{5}
$$

Step 2: Move all terms with $m$ to one side, constants to the other

Subtract $\frac{1}{5}m$ from both sides:
$$
-\frac{4}{3} = m - \frac{1}{5}m - \frac{2}{5}
$$

Simplify right side:
$$
m - \frac{1}{5}m = \frac{4}{5}m
$$

So:
$$
-\frac{4}{3} = \frac{4}{5}m - \frac{2}{5}
$$

Step 3: Add $\frac{2}{5}$ to both sides
$$
-\frac{4}{3} + \frac{2}{5} = \frac{4}{5}m
$$

Find common denominator (15):
$$
-\frac{4}{3} = -\frac{20}{15},\quad \frac{2}{5} = \frac{6}{15}
\Rightarrow -\frac{20}{15} + \frac{6}{15} = -\frac{14}{15}
$$

So:
$$
-\frac{14}{15} = \frac{4}{5}m
$$

Step 4: Solve for $m$
$$
m = -\frac{14}{15} \div \frac{4}{5} = -\frac{14}{15} \times \frac{5}{4} = -\frac{70}{60} = -\frac{7}{6}
$$

✔ Answer: $m = -\frac{7}{6}$

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✔ Final Answers:

1. $x = 4$
2. $a = 16$
3. $v = -16$
4. $v = \frac{26}{63}$
5. $t = -\frac{5}{8}$
6. $m = -\frac{7}{6}$

Let me know if you'd like a visual explanation or check!