Good morning! I am trying to help my nephew who because of seizures when he was younger has a hard time understanding math. I need step-by-step (written in words) on how to do two-step equations (distributive properties). 3(c+5)=12. 5(4d+8)=40.
-(2k-11)=7. 3/4(4x+8)=-12 -4(3x-2)=-32. 1/3(9c-36)=-9
Any help would be greatly appreciated!
step 1: remove the parentheses, by applying the distributive property
step2: collect all the variable stuff on one side, by adding/subtracting the constants
step3: divide by the coefficient to isolate the variable value
3(c+5) = 12
1:3c+15 = 12
2:3c = 12-15 = -3
3: c = -1
3/4 (4x+8) -12
3x+6 = -12
3x = -18
x = -6
and so on
Good morning! I'm here to help you with two-step equations involving distributive properties. Let's solve them step by step:
First equation: 3(c + 5) = 12
Step 1: Distribute the 3 to both terms inside the parentheses.
3 * c + 3 * 5 = 12
3c + 15 = 12
Step 2: Move the constant term (15) to the other side of the equation by subtracting it from both sides.
3c + 15 - 15 = 12 - 15
3c = -3
Step 3: Divide both sides by the coefficient of c (3) to isolate c.
3c / 3 = -3 / 3
c = -1
So the solution to the first equation is c = -1.
Let's move on to the second equation: 5(4d + 8) = 40
Step 1: Distribute the 5 to both terms inside the parentheses.
5 * 4d + 5 * 8 = 40
20d + 40 = 40
Step 2: Move the constant term (40) to the other side of the equation by subtracting it from both sides.
20d + 40 - 40 = 40 - 40
20d = 0
Step 3: Divide both sides by the coefficient of d (20) to isolate d.
20d / 20 = 0 / 20
d = 0
So the solution to the second equation is d = 0.
Let's continue with the third equation: -(2k - 11) = 7
Step 1: Distribute the negative sign to both terms inside the parentheses.
-1 * 2k + -1 * -11 = 7
-2k + 11 = 7
Step 2: Move the constant term (11) to the other side of the equation by subtracting it from both sides.
-2k + 11 - 11 = 7 - 11
-2k = -4
Step 3: Divide both sides by the coefficient of k (-2) to isolate k.
-2k / -2 = -4 / -2
k = 2
So the solution to the third equation is k = 2.
Let's move on to the fourth equation: 3/4(4x + 8) = -12
Step 1: Distribute the fraction (3/4) to both terms inside the parentheses.
(3/4) * 4x + (3/4) * 8 = -12
(3/1)(4/4)x + (3/4)(8/1) = -12
3x + 6 = -12
Step 2: Move the constant term (6) to the other side of the equation by subtracting it from both sides.
3x + 6 - 6 = -12 - 6
3x = -18
Step 3: Divide both sides by the coefficient of x (3) to isolate x.
3x / 3 = -18 / 3
x = -6
So the solution to the fourth equation is x = -6.
Moving on to the fifth equation: -4(3x - 2) = -32
Step 1: Distribute the -4 to both terms inside the parentheses.
-4 * 3x - 4 * -2 = -32
-12x + 8 = -32
Step 2: Move the constant term (8) to the other side of the equation by subtracting it from both sides.
-12x + 8 - 8 = -32 - 8
-12x = -40
Step 3: Divide both sides by the coefficient of x (-12) to isolate x.
-12x / -12 = -40 / -12
x = 10/3 or 3.33 (rounded to two decimal places)
So the solution to the fifth equation is x = 10/3 or approximately 3.33.
Finally, let's solve the sixth equation: 1/3(9c - 36) = -9
Step 1: Distribute the fraction (1/3) to both terms inside the parentheses.
(1/3) * 9c - (1/3) * 36 = -9
(1/1)(9/3)c - (1/3)(36/1) = -9
3c - 12 = -9
Step 2: Move the constant term (12) to the other side of the equation by adding it to both sides.
3c - 12 + 12 = -9 + 12
3c = 3
Step 3: Divide both sides by the coefficient of c (3) to isolate c.
3c / 3 = 3 / 3
c = 1
So the solution to the sixth equation is c = 1.
I hope this step-by-step explanation helps your nephew with math. If you have any more questions, feel free to ask!