The solution to the given equation is t = 62.
We have,
Let's simplify the given equation step by step:
8(t + 2) - 3(t - 4) = 6(t - 7) + 8
Step 1: Apply the distributiveproperty by multiplying each term inside the parentheses by the coefficient outside the parentheses:
8t + 16 - 3t + 12 = 6t - 42 + 8
Simplifying the equation further:
8t - 3t + 16 + 12 = 6t - 42 + 8
Step 2: Combine liketerms on both sides of the equation:
(8t - 3t) + 28 = 6t - 34
Simplifying the equation further:
5t + 28 = 6t - 34
Step 3: To isolate the variable t, we will move all terms containing t to one side and the constants to the other side:
5t - 6t = -34 - 28
Simplifying the equation further:
-1t = -62
Step 4: Since -1t is equivalent to -t, we can rewrite the equation as:
-t = -62
Step 5: To solve for t, we need to multiply both sides of the equation by -1 to eliminate the negative sign:
(-1)(-t) = (-1)(-62)
Simplifying the equation further:
t = 62
Therefore,
The solution to the given equation is t = 62.
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