Welcome to your ACT 1 Alg: Solve equations and inequalities in 1 variable

$Q_{1}:$ For what values of $x$ is $5x+97=47$?

$Q_{2}:$ For what values of $x$ is $0.8x-2.3=0.5$?

$Q_{3}:$ For what values of $x$ is $0.2x+0.3=1.9$?

$Q_{4}:$ For what values of $x$ is $\frac{2x}{5}+\frac{6}{5}=5$?

$Q_{5}:$ The solution of $\frac{1}{2}x+3(x-2)=2(x+1)+1$ is

$Q_{6}:$ If $z$ is an integer and the average (arithmetic mean) of $1, 2, 3$, and $z$ is less than $20$, what is the greatest possible value of $z$?

$Q_{7}: \frac{3}{4}-\frac{5}{x}=\frac{7}{x}$, the value of $x$ is

$Q_{8}:$ For what value of $y$ is $\frac{3}{4}-\frac{5}{y}>\frac{7}{y}$?

$Q_{9}:$ For what values of $x$ is $3 \left | x + 5 \right | -5< 7$

$Q_{10}:$ $ 4(\sqrt[3]{x}+1)=\sqrt[3]{x} +25 $, the value of $x$ is

$Q_{11}:$ If $\frac{x+3}{2}+3x=5(x-3)+\frac{(x+23)}{5}$ , what is the value of $x$?

$Q_{12}:$ If $ax - b = c - dx$, what is the value of $x$ in terms of $a, b, c,$ and $d$ ?

$Q_{13}:$ Which of the following inequalities is equivalent to $0.6( y-7) - 0.3y > 1.8 +0.9y$ ?

$Q_{14}:$ One half of a number decreased by $3$ is at most $−5$. Which of the following inequalities represents the statement?

$Q_{15}:$Which of the following numbers is NOT a solution to the inequality $\frac{(3b+5)}{-2}\geq (b-8)$ ?

$Q_{16}:$ Nine is not more than the sum of a number and 17. Which of the following inequalities represents the statement?

$Q_{17}:$ Four times the greatest of three consecutive odd integers exceeds three times the least by 31. What is the greatest of the three consecutive odd integers?

$Q_{18}:$ The sum of four consecutive odd integers is 296 . What is the greatest of the four consecutive odd integers?

$Q_{19}:$ Eight less than four times the number $t$ is twenty. What is the value of $t$?

$Q_{20}:$ A number $K$ is decreased by $23$ and then multiplied by $\frac{1}{2}$. The result is $8$ more than twice the number $K$.

$Q_{21}:$ There are one hundred forty-two students in a high school band. These students represent two ninth of the total students in the high school. How many students attend the school?

$Q_{22}:$ A $48£$ shirts costs $22£$ more than one half the cost of a pair of pants. How much does the pair of pants cost?

$Q_{23}: \frac{(15-6y)}{3}=5-ay$ . If the linear equation is an identity, what is the value of a ?

$Q_{24}: 4h+13=7(h-2)+dh $ If the linear equation has no solution, which of the following could be the value of $d$ ?

$Q_{25}:$ Ayah Car Rental charges a flat fee of $40.00£$ per day plus $0.54£$ per mile to rent a car. Malk Car Rental charges a flat fee of $65.00£$ per day plus $0.36£$ per mile to rent a car. If a car is rented for three days, at least how many miles would you have to drive, to the nearest mile, to make the Ayah Car Rental company the better option?

$Q_{26}:$ The number of students in a Math class is four fifths the number of students in a English class. The total number of students in both classes does not exceed 54. What is the greatest possible number of students in the English class?

$Q_{27}:$ Which of the following inequalities represents the same set as the set graphed on the number line shown?