Solve each of these equations. Explain your reasoning.
1.2(3x+2)=2x+28
2.5y+13=-43-3y
3.4(2a+2)8(2-3a)
2(3x+2)=2x+28
6x + 4 = 2x + 28
4x = 24
x = 6
OK. I did the first one. Now you can do the other two. We'll be glad to check your answer.
1. distribute the 2 into the brackets to obtain
6x + 4 = 2x + 28
Then take your letters(variables) to one side and your numbers to the other.
2. Just add 3y to both sides to balance the equation
5y+3y+13 = 43 - 3y +3y
8y+13 = 43
Now subtract 13 from both sides to balance the equation and continue...
3. I believe you have left out the equal sign. Distribute the 4 into the left hand side brackets and the 8 into the right hand side brackets. Then get your letters(variables) to one side and your numbers to the other...
Sure! Let's solve each of these equations step by step:
1. 2(3x+2) = 2x+28
To start, let's simplify the equation by distributing the 2 on the left side:
6x + 4 = 2x + 28
Next, let's isolate the variables on one side and the constants on the other side. We can achieve this by subtracting 2x from both sides:
6x - 2x + 4 = 2x - 2x + 28
Simplifying further, we get:
4x + 4 = 28
Now, let's isolate the variable term by subtracting 4 from both sides:
4x + 4 - 4 = 28 - 4
Simplifying further, we get:
4x = 24
Finally, to solve for x, we divide both sides of the equation by 4:
(4x)/4 = 24/4
Simplifying, we get:
x = 6
Therefore, the value of x in the equation 2(3x+2) = 2x+28 is 6.
2. 5y + 13 = -43 - 3y
To solve this equation, let's begin by isolating the variable term on one side and the constant term on the other side. We can achieve this by adding 3y to both sides and subtracting 13 from both sides:
5y + 3y + 13 - 13 = -43 - 3y + 3y
Simplifying further, we get:
8y = -43
Next, let's solve for y by dividing both sides of the equation by 8:
(8y)/8 = -43/8
Simplifying, we get:
y = -5.375
Therefore, the value of y in the equation 5y + 13 = -43 - 3y is approximately -5.375.
3. 4(2a+2)8(2-3a)
To solve this equation, let's distribute the constants and simplify:
8a + 8 + 16 - 24a
Combining like terms, we get:
-16a + 24
Therefore, the simplified form of 4(2a+2)8(2-3a) is -16a + 24.