1. 2(3x + 5) = 46
4
5
6
7
2. 1/2x + 1/4x = 16
16
21.3
32
64
3. 6 - x - x = 18
-6
6
9
-9
4. 4x - 3/5 = 2/5
1/5
5/5
1/2
1/4
My answers:
1. 6
2. 21.3
3. ????
4. 1/4
I have no idea how to solve 3! Can you please explain? Thank you
6 - x - x = 18
6 - 2x = 18
-2x = 12
x = -6
check:
6 - (-6) - (-6) = 6+6+6 = 18
the others look good.
Can't imagine why #3 threw you. It's the most straightforward of them all.
6 - x - x = 18
-2x = 12
x = -6
Your answers are correct.
Thank you! That helped a lot! I have no idea why 3 was hard for me...
Certainly! Let's go through each question and explain how to find the answer.
1. To solve the equation 2(3x + 5) = 46, you can start by distributing the 2 to both terms inside the parentheses. This gives you 6x + 10 = 46. Next, you want to isolate the variable term, so subtract 10 from both sides of the equation. This gives you 6x = 36. Finally, divide both sides of the equation by 6 to solve for x. Thus, the correct answer is x = 6.
2. To solve the equation 1/2x + 1/4x = 16, you need to first simplify the fractions by finding a common denominator. The least common denominator (LCD) for 2 and 4 is 4. Multiplying the first term by 2/2 and the second term by 1/1 gives you 2/4x + 1/4x = 16. Combining the like terms, you have 3/4x = 16. To isolate x, multiply both sides of the equation by 4/3. This gives you x = (16)(4/3), which simplifies to x = 64/3 or approximately 21.3.
3. The equation 6 - x - x = 18 involves solving for x when there are multiple instances of x. To start simplifying, combine the x terms on the left side by subtracting them. This gives you 6 - 2x = 18. Next, you want to isolate the variable term by subtracting 6 from both sides of the equation. This gives you -2x = 12. Finally, divide both sides of the equation by -2 to solve for x. Thus, the correct answer is x = -6.
4. To solve the equation 4x - 3/5 = 2/5, you want to isolate the x term. Start by adding 3/5 to both sides of the equation. This gives you 4x = 2/5 + 3/5. Simplifying the right side of the equation, you have 4x = 5/5, which is equivalent to 1. Finally, divide both sides of the equation by 4 to solve for x. Therefore, the correct answer is x = 1/4.
Based on your answers:
1. You got it right! The answer is 6.
2. You got it right! The answer is 21.3.
3. Oops! The correct answer is x = -6, not 9.
4. Oops! The correct answer is x = 1/4, not 1/5.
Keep practicing and you'll become more comfortable with solving equations involving variables!