QuestionSolve the equations and verify your answers:
1. $\frac{5 r}{2}-6=19$
2. $\frac{n}{3}-8=-2$
3. $5+\frac{x}{4}=1$
4. $-\frac{h}{3}-4=13$
5. $5(1+n)=-5$

Studdy Solution
Assumptions1. The equations are linear equations. . The solutions to the equations are real numbers.
Problem29First, we need to isolate the term with the variable on one side of the equation. We can do this by adding6 to both sides of the equation.
$$\frac{5 r}{} -6 +6 =19 +6$$3implify the equation.
$$\frac{5 r}{} =25$$4To solve for r, multiply both sides of the equation by/5.
$$r = \frac{25}{5} \times \frac{}{5}$$5Calculate the value of r.
$$r =10$$Problem306First, we need to isolate the term with the variable on one side of the equation. We can do this by adding8 to both sides of the equation.
$$\frac{n}{3} -8 +8 = - +8$$7implify the equation.
$$\frac{n}{3} =6$$8To solve for n, multiply both sides of the equation by3.
$$n =6 \times3$$9Calculate the value of n.
$$n =18$$Problem3110First, we need to isolate the term with the variable on one side of the equation. We can do this by subtracting5 from both sides of the equation.
$$5 + \frac{x}{4} -5 =1 -5$$11implify the equation.
$$\frac{x}{4} = -4$$12To solve for x, multiply both sides of the equation by4.
$$x = -4 \times4$$13Calculate the value of x.
$$x = -16$$Problem3214First, we need to isolate the term with the variable on one side of the equation. We can do this by adding4 to both sides of the equation.
$$-\frac{h}{3} -4 +4 =13 +4$$15implify the equation.
$$-\frac{h}{3} =17$$16To solve for h, multiply both sides of the equation by -3.
$$h =17 \times -3$$17Calculate the value of h.
$$h = -51$$Problem3318First, we need to distribute the5 into the parentheses.
$$5 \times1 +5 \times n = -5$$19implify the equation.
$$5 +5n = -5$$20To isolate the term with the variable, subtract5 from both sides of the equation.
$$5 +5n -5 = -5 -5$$21implify the equation.
$$5n = -10$$22To solve for n, divide both sides of the equation by5.
$$n = \frac{-10}{5}$$23Calculate the value of n.
$$n = -$$The solutions to the equations are r=10, n=18, x=-16, h=-51, n=-.