Answer:
t = 12.
Explanation:
PART 1:
To solve two-step equations without parentheses, follow these steps:
1. Start by isolating the variable term on one side of the equation. To do this, eliminate any constant terms (numbers without variables) by performing the inverse operation. For example, if there is a constant term of 3 added to the variable term, you would subtract 3 from both sides of the equation.
2. After isolating the variable term, you will have a one-step equation. To solve for the variable, perform the inverse operation on the variable term. For instance, if the variable is multiplied by 5, you would divide both sides of the equation by 5.
3. Simplify both sides of the equation to find the value of the variable. This may involve combining like terms or performing arithmetic operations.
4. Check your solution by substituting the value of the variable back into the original equation. If the equation holds true when the value is substituted, then your solution is correct. If not, you may have made an error during the solving process and should retrace your steps.
Here's an example to illustrate these steps:
Given the equation: 2x + 7 = 15
Step 1: Isolate the variable term. Since there is a constant term of 7 added to the variable term 2x, we can eliminate it by subtracting 7 from both sides of the equation:
2x + 7 - 7 = 15 - 7
2x = 8
Step 2: Solve the one-step equation. The variable term 2x is being multiplied by 2, so we need to perform the inverse operation by dividing both sides of the equation by 2:
2x/2 = 8/2
x = 4
Step 3: Simplify. The variable x is equal to 4.
Step 4: Check the solution. Substitute x = 4 back into the original equation:
2(4) + 7 = 15
8 + 7 = 15
15 = 15
Since the equation holds true, the solution x = 4 is correct.
Remember to follow these steps systematically when solving two-step equations without parentheses. Practice with more examples to reinforce your understanding.
PART 2:
To solve for t in the equation t/3 - 2 = 2, follow these steps:
1. Start by isolating the variable term by eliminating the constant term. In this case, the constant term is -2. To eliminate it, add 2 to both sides of the equation:
t/3 - 2 + 2 = 2 + 2
2. Simplify the equation. On the left side, the -2 and +2 cancel each other out, leaving you with:
t/3 = 4
3. Solve the equation by performing the inverse operation. The variable term t is divided by 3, so to undo the division, you need to multiply both sides of the equation by 3:
t/3 * 3 = 4 * 3
4. Simplify the equation further. On the left side, the t/3 and 3 cancel each other out, leaving you with:
t = 12
The solution to the equation t/3 - 2 = 2 is t = 12.
Remember to check your solution by substituting t = 12 back into the original equation to ensure that it holds true. In this case, when you substitute 12 for t, you get:
12/3 - 2 = 2
4 - 2 = 2
2 = 2
Since the equation holds true, the solution t = 12 is correct.