Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

1. \(4(2x+3)=2+(-4-5x)\)
2. \(4(-2x-1)=14-(14-5x)\)
3. \(5(2x+3)=-10-(8-3x)\)
4. \(3(-5x+4)=-10+(-9-2x)\)
5. \(5(-6x+1)=-1+(-5+x)\)
6. \(3(-4x-7)=7-(13+x)\)
7. \(3(-4x-6)=-6-(12+x)\)
8. \(4(-x+4)=-9-(-7-3x)\)
9. \(3(-6x-3)=-1-(4-5x)\)
10. \(4(-5x-7)=-14-(-3+x)\)
11. \(2(4x-6)=-10+(5-5x)\)
12. \(6(4x-5)=15+(-2+x)\)

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (2x+3)& = & 2 \color{red}{+} (-4-5x) \\\Leftrightarrow & 8x+12& = &2-4-5x \\\Leftrightarrow & 8x \color{red}{+12} & = &-2 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &-2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & 8x+5x& = &-2-12 \\\Leftrightarrow & 13x& = &-14 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-14}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-14}{13} & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-2x-1)& = & 14 \color{red}{-} (14-5x) \\\Leftrightarrow & -8x-4& = &14-14+5x \\\Leftrightarrow & -8x \color{red}{-4} & = &0 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{-4} \color{blue}{+4} \color{blue}{-5x} & = &0 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+4} \\\Leftrightarrow & -8x-5x& = &0+4 \\\Leftrightarrow & -13x& = &4 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{4}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-4}{13} & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (2x+3)& = & -10 \color{red}{-} (8-3x) \\\Leftrightarrow & 10x+15& = &-10-8+3x \\\Leftrightarrow & 10x \color{red}{+15} & = &-18 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+15} \color{blue}{-15} \color{blue}{-3x} & = &-18 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-15} \\\Leftrightarrow & 10x-3x& = &-18-15 \\\Leftrightarrow & 7x& = &-33 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-33}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-33}{7} & & \\ & V = \left\{ \frac{-33}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-5x+4)& = & -10 \color{red}{+} (-9-2x) \\\Leftrightarrow & -15x+12& = &-10-9-2x \\\Leftrightarrow & -15x \color{red}{+12} & = &-19 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+12} \color{blue}{-12} \color{blue}{+2x} & = &-19 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-12} \\\Leftrightarrow & -15x+2x& = &-19-12 \\\Leftrightarrow & -13x& = &-31 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-31}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{31}{13} & & \\ & V = \left\{ \frac{31}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-6x+1)& = & -1 \color{red}{+} (-5+x) \\\Leftrightarrow & -30x+5& = &-1-5+x \\\Leftrightarrow & -30x \color{red}{+5} & = &-6 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+5} \color{blue}{-5} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-5} \\\Leftrightarrow & -30x-x& = &-6-5 \\\Leftrightarrow & -31x& = &-11 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-11}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{11}{31} & & \\ & V = \left\{ \frac{11}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-4x-7)& = & 7 \color{red}{-} (13+x) \\\Leftrightarrow & -12x-21& = &7-13-x \\\Leftrightarrow & -12x \color{red}{-21} & = &-6 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-21} \color{blue}{+21} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+21} \\\Leftrightarrow & -12x+x& = &-6+21 \\\Leftrightarrow & -11x& = &15 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{15}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-15}{11} & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-4x-6)& = & -6 \color{red}{-} (12+x) \\\Leftrightarrow & -12x-18& = &-6-12-x \\\Leftrightarrow & -12x \color{red}{-18} & = &-18 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -12x+x& = &-18+18 \\\Leftrightarrow & -11x& = &0 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{0}{ \color{red}{-11} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-x+4)& = & -9 \color{red}{-} (-7-3x) \\\Leftrightarrow & -4x+16& = &-9+7+3x \\\Leftrightarrow & -4x \color{red}{+16} & = &-2 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+16} \color{blue}{-16} \color{blue}{-3x} & = &-2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-16} \\\Leftrightarrow & -4x-3x& = &-2-16 \\\Leftrightarrow & -7x& = &-18 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-18}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{18}{7} & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-6x-3)& = & -1 \color{red}{-} (4-5x) \\\Leftrightarrow & -18x-9& = &-1-4+5x \\\Leftrightarrow & -18x \color{red}{-9} & = &-5 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-9} \color{blue}{+9} \color{blue}{-5x} & = &-5 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+9} \\\Leftrightarrow & -18x-5x& = &-5+9 \\\Leftrightarrow & -23x& = &4 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{4}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-4}{23} & & \\ & V = \left\{ \frac{-4}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-5x-7)& = & -14 \color{red}{-} (-3+x) \\\Leftrightarrow & -20x-28& = &-14+3-x \\\Leftrightarrow & -20x \color{red}{-28} & = &-11 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & -20x+x& = &-11+28 \\\Leftrightarrow & -19x& = &17 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{17}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-17}{19} & & \\ & V = \left\{ \frac{-17}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (4x-6)& = & -10 \color{red}{+} (5-5x) \\\Leftrightarrow & 8x-12& = &-10+5-5x \\\Leftrightarrow & 8x \color{red}{-12} & = &-5 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &-5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & 8x+5x& = &-5+12 \\\Leftrightarrow & 13x& = &7 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{7}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{7}{13} & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (4x-5)& = & 15 \color{red}{+} (-2+x) \\\Leftrightarrow & 24x-30& = &15-2+x \\\Leftrightarrow & 24x \color{red}{-30} & = &13 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 24x-x& = &13+30 \\\Leftrightarrow & 23x& = &43 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{43}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{43}{23} & & \\ & V = \left\{ \frac{43}{23} \right\} & \\\end{align}\)