[No-Calc] Question Easy
What value of x is the solution to the equation x+10=3 ?
▶️Answer/Explanation
To solve the equation \(x+10=3\), we need to isolate \(x\) by subtracting 10 from both sides:
\[x + 10 – 10 = 3 – 10\]
\[x = -7\]
So, the solution to the equation is \(x = -7\).
[No-Calc] Question Easy
\(\left | x+3=6 \right |\)
What is the positive solution to the given equation?
A. 2
B. 3
C. 9
D. 18
▶️Answer/Explanation
To find the positive solution to the equation \( |x+3| = 6 \), we consider both the positive and negative cases for the absolute value.
Positive case:
\[ x + 3 = 6 \]
\[ x = 6 – 3 \]
\[ x = 3 \]
Negative case:
\[ -(x + 3) = 6 \]
\[ -x – 3 = 6 \]
\[ -x = 6 + 3 \]
\[ -x = 9 \]
\[ x = -9 \]
Since we’re looking for the positive solution, the answer is \( x = 3 \), which corresponds to option B.
[No-Calc] Question Easy
If 2(x − 4) = x , what value of x makes the equation true?
▶️Answer/Explanation
D) 8
We are given the equation \( 2(x – 4) = x \) and need to find the value of \( x \) that makes the equation true.
Distributing the 2 on the left-hand side:
\[
2(x – 4) = 2x – 8
\]
So, the equation becomes:
\[
2x – 8 = x
\]
Subtract \( x \) from both sides to isolate \( x \):
Add 8 to both sides to solve for \( x \):
[Calc] Question Easy
Which equation has the same solution as 8x = 2x + 12?
▶️Answer/Explanation
D) 6x = 12
To find the equation that has the same solution as \(8x = 2x + 12\):
Solve the original equation for \(x\):
Check each option to see which one also has \(x = 2\) as a solution:
Option A: \(10x = -12\)
\[
x = -\frac = -\frac
\]
This does not match \(x = 2\).
Option B: \(10x = 12\)
\[
x = \frac = \frac
\]
This does not match \(x = 2\).
Option C: \(6x = -12\)
\[
x = -2
\]
This does not match \(x = 2\).
Option D: \(6x = 12\)
\[
x = 2
\]
This matches the solution of the original equation.
[Calc] Question Easy
Line segment \(A C\) has a length of 120 and contains point \(B\). If \(A B=5 x+20\) and \(B C=6 x-10\), which equation shows the relationship between the lengths of line segments \(A B, B C\), and \(A C\) ?
A) \(5 x+20=120\)
B) \(6 x-10=120\)
C) \((5 x+20)-(6 x-10)=120\)
D) \((5 x+20)+(6 x-10)=120\)
▶️Answer/Explanation
We need to find the equation that represents the relationship between the lengths of the line segments \(AB\), \(BC\), and \(AC\).Since \(AC = AB + BC\):
\[ AC = 120 \]
\[ AB + BC = 120 \]
\[ (5x + 20) + (6x – 10) = 120 \]
Simplifying:
\[ 5x + 20 + 6x – 10 = 120 \]
\[ 11x + 10 = 120 \]
Therefore, the correct equation is:
\[ (5x + 20) + (6x – 10) = 120 \]
So the answer is:
\[ \boxed \]
[Calc] Question Easy
2 |4 – x | + 3 | 4 – x | = 25
What is the positive solution to the given equation ?
▶️Answer/Explanation
To find the positive solution to the equation \(2|4-x| + 3|4-x| = 25\), we can simplify and solve it step-by-step.
2. Divide both sides by 5:
\[
|4-x| = 5
\]
3. Solve the absolute value equation:
\[
4-x = 5 \quad \text \quad 4-x = -5
\]
Thus, the positive solution is:
\[ \boxed \]
[No-Calc] Question Easy
2p + 6 = 8 + 7p
What value of p satisfies the given equation?
▶️Answer/Explanation
We need to solve the equation \( 2p + 6 = 8 + 7p \) for \( p \).
Start with the given equation:
\[
2p + 6 = 8 + 7p
\]
Subtract \( 2p \) from both sides:
\[
6 = 8 + 5p
\]
[No-Calc] Question Easy
4(x + 1) = 6 + 2(x + 1)
If x is the solution to the given equation, what is the value of x + 1 ?
▶️Answer/Explanation
B) 3
Let’s solve each problem step by step:
\[
4(x+1) = 6+2(x+1)
\]
\[
4x + 4 = 6 + 2x + 2
\]
\[
4x + 4 = 2x + 8
\]
Subtract \(2x\) from both sides:
\[
2x + 4 = 8
\]
Subtract \(4\) from both sides:
\[
2x = 4
\]
divide both sides by \(2\):
\[
x = 2
\]
If \(x = 2\), then \(x+1 = 3\).
So, the correct answer is B) 3.