Sharpen your ACT Math skills with this focused quiz on algebra and linear equations. Tackle key concepts like solving equations, understanding slopes, graph interpretation, and applying properties of algebraic expressions for improved test readiness.
What is the solution to the equation 3x - 5 = 16?
Explanation: To solve 3x - 5 = 16, first add 5 to both sides to get 3x = 21. Then, divide both sides by 3 to find x = 7, which is correct. Choosing x = 11 skips a subtraction step, x = 21 results from misreading the equation, while x = -7 is the opposite and not a logical answer in this context.
If a line passes through the points (2, 5) and (4, 9), what is the slope of the line?
Explanation: The slope is calculated as (9 - 5) divided by (4 - 2), which gives 4 divided by 2, resulting in a slope of 2. A slope of 3 uses the numerator only, 4 ignores the correct calculation, and 1 underestimates the difference between the points.
For the equation y = -3x + 6, what is the y-intercept?
Explanation: In the slope-intercept form y = mx + b, the b-value represents the y-intercept, which is 6 in this equation. A value of 3 confuses the coefficient of x, -3 is the slope, and -6 is unrelated to the intercept.
What does 2(4x - 7) simplify to?
Explanation: Applying the distributive property, multiply 2 by both 4x and -7 to get 8x - 14. Choosing 8x - 7 ignores multiplying -7, 8x + 14 incorrectly changes the sign, and 4x - 14 fails to multiply 4x by 2.
In the equation 2x + 9 = x - 5, what is the value of x?
Explanation: First subtract x from both sides to obtain x + 9 = -5, then subtract 9, resulting in x = -14. The value x = 14 comes from forgetting the negative sign, x = 4 incorrectly switches operations, and x = -4 confuses the terms when isolating x.