Solve using distributive property
(Shaow all Work)
8t-4+3(y+7)=6y-3(y-3)
To solve the given expression using the distributive property, you need to distribute the coefficients to all the terms inside the parentheses. Let's break it down step by step:
Given expression: 8t - 4 + 3(y + 7) = 6y - 3(y - 3)
Step 1: Distribute the coefficient 3 to both terms inside the parentheses: 3 * y = 3y and 3 * 7 = 21.
So, the expression becomes: 8t - 4 + 3y + 21 = 6y - 3(y - 3)
Step 2: Distribute the coefficient -3 to both terms inside the parentheses: -3 * y = -3y and -3 * -3 = 9.
The expression now becomes: 8t - 4 + 3y + 21 = 6y - 3y + 9
Step 3: Combine like terms on both sides:
On the left side, combine -4 and 21 to get 17: 8t + 17 + 3y = 6y - 3y + 9
Simplifying further on the left side: 8t + 3y + 17 = 3y + 9
Step 4: Simplify the right side by combining like terms:
Combine 6y and -3y on the right side to get 3y: 8t + 3y + 17 = 3y + 9
Step 5: Isolate the y term on one side of the equation by subtracting 3y from both sides:
8t + 3y - 3y + 17 = 3y - 3y + 9
Simplifying further: 8t + 17 = 9
Step 6: Finally, isolate the variable t by subtracting 17 from both sides:
8t + 17 - 17 = 9 - 17
Simplifying further: 8t = -8
Step 7: Solve for t by dividing both sides by 8:
(8t)/8 = -8/8
Thus, t = -1.
Therefore, the solution to the equation is t = -1.