Null points

Calculate the roots of the equation:

3x+4+3x+5+2x+4=303 |x +4| +3 |x +5| +2 |x +4| = 30


Correct result:

number of roots:  2
x1 =  -8.13
x2 =  -0.63

Solution:

 x(;5>3(x+4)3(x+5)2(x+4)=30x=8.125(;5> x(5;4>3(x+4)+3(x+5)2(x+4)=30x=17.5(5;4> x(4;+)3(x+4)+3(x+5)+2(x+4)=30x=0.625(4;+) P={8.125,0.625} \ \\ x \in \left(-\infty; -5\right> \Rightarrow -3 (x +4) -3 (x +5) -2 (x +4) = 30 \Rightarrow x = -8.125 \in \left(-\infty; -5\right> \ \\ x \in \left(-5; -4\right> \Rightarrow -3 (x +4) +3 (x +5) -2 (x +4) = 30 \Rightarrow x = -17.5 \notin \left(-5; -4\right> \ \\ x \in \left(-4; +\infty\right) \Rightarrow 3 (x +4) +3 (x +5) +2 (x +4) = 30 \Rightarrow x = -0.625 \in \left(-4; +\infty\right) \ \\ P = \{ -8.125, -0.625 \}



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!


Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Tips to related online calculators
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?

You need to know the following knowledge to solve this word math problem:

Next similar math problems:

  • Geometric sequence 5
    sequence About members of geometric sequence we know: ? ? Calculate a1 (first member) and q (common ratio or q-coefficient)
  • Ball game
    lopta_3 Richard, Denis and Denise together scored 932 goals. Denis scored 4 goals over Denise but Denis scored 24 goals less than Richard. Determine the number of goals for each player.
  • Stones 3
    stones Simiyu and Nasike each collected a number of stones in an arithmetic lesson. If Simiyu gave Nasike 5 stones, Nasike would have twice as many stones as Simiyu. If initially, Simiyu had five stones less than Nasike how many stones did each have?
  • Warehouses
    silo_3 In the three warehouses, a total of 70 tons of grain was stored. In the second warehouse was stored 8.5t less and in the third 3.5t more than in the first. How many tons of grain was stored in each warehouse?
  • Men, women and children
    regiojet On the trip went men, women and children in the ratio 2:3:5 by bus. Children pay 60 crowns and adults 150. How many women were on the bus when a bus was paid 4,200 crowns?
  • Children
    children_3 The group has 42 children. There are 4 more boys than girls. How many boys and girls are in the group?
  • Isosceles trapezoid
    lichobeznik_2 Perimeter of the isosceles trapezoid is 48 cm. One side is two times greater than the second side. Determine the dimensions of the trapezoid.
  • Football match 4
    futball_ball In a football match with the Italy lost 3 goals with Germans. Totally fell 5 goals in the match. Determine the number of goals of Italy and Germany.
  • Integer
    abs1 Find the integer whose distance on the numerical axis from number 1 is two times smaller as the distance from number 6.
  • Equation with abs value
    abs_graph How many solutions has the equation ? in the real numbers?
  • Asymptote
    asymptote What is the vertical asymptote of ?
  • Intercept with axis
    log_10 F(x)=log(x+4)-2, what is the x intercept
  • Linsys2
    linear_eq_3 Solve two equations with two unknowns: 400x+120y=147.2 350x+200y=144
  • Gasoline canisters
    fuel_4 35 liters of gasoline is to be divided into 4 canisters so that in the third canister will have 5 liters less than in the first canister, the fourth canister 10 liters more than the third canister and the second canister half of that in the first canis
  • Legs
    rak Cancer has 5 pairs of legs. The insect has 6 legs. 60 animals have a total of 500 legs. How much more are cancers than insects?
  • AP - basics
    ap Determine first member and differentiate of the the following sequence: a3-a5=24 a4-2a5=61
  • Three unknowns
    matrix_1 Solve the system of linear equations with three unknowns: A + B + C = 14 B - A - C = 4 2A - B + C = 0