Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (6x+3)& = & 10 \color{red}{+} (10+x) \\\Leftrightarrow & 24x+12& = &10+10+x \\\Leftrightarrow & 24x \color{red}{+12} & = &20 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &20 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 24x-x& = &20-12 \\\Leftrightarrow & 23x& = &8 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{8}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{8}{23} & & \\ & V = \left\{ \frac{8}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-3x-1)& = & -3 \color{red}{+} (11-5x) \\\Leftrightarrow & -18x-6& = &-3+11-5x \\\Leftrightarrow & -18x \color{red}{-6} & = &8 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &8 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & -18x+5x& = &8+6 \\\Leftrightarrow & -13x& = &14 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{14}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-14}{13} & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-x-3)& = & 1 \color{red}{+} (11+x) \\\Leftrightarrow & -6x-18& = &1+11+x \\\Leftrightarrow & -6x \color{red}{-18} & = &12 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -6x-x& = &12+18 \\\Leftrightarrow & -7x& = &30 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{30}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-30}{7} & & \\ & V = \left\{ \frac{-30}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (2x-3)& = & 15 \color{red}{+} (-1+x) \\\Leftrightarrow & 12x-18& = &15-1+x \\\Leftrightarrow & 12x \color{red}{-18} & = &14 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 12x-x& = &14+18 \\\Leftrightarrow & 11x& = &32 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{32}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{32}{11} & & \\ & V = \left\{ \frac{32}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-x+2)& = & -9 \color{red}{-} (-2-5x) \\\Leftrightarrow & -6x+12& = &-9+2+5x \\\Leftrightarrow & -6x \color{red}{+12} & = &-7 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &-7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & -6x-5x& = &-7-12 \\\Leftrightarrow & -11x& = &-19 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-19}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{19}{11} & & \\ & V = \left\{ \frac{19}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-3x+2)& = & -8 \color{red}{-} (-9-5x) \\\Leftrightarrow & -18x+12& = &-8+9+5x \\\Leftrightarrow & -18x \color{red}{+12} & = &1 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &1 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & -18x-5x& = &1-12 \\\Leftrightarrow & -23x& = &-11 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-11}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{11}{23} & & \\ & V = \left\{ \frac{11}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (5x+1)& = & 15 \color{red}{-} (-2-2x) \\\Leftrightarrow & 15x+3& = &15+2+2x \\\Leftrightarrow & 15x \color{red}{+3} & = &17 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+3} \color{blue}{-3} \color{blue}{-2x} & = &17 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-3} \\\Leftrightarrow & 15x-2x& = &17-3 \\\Leftrightarrow & 13x& = &14 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{14}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{14}{13} & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (2x-6)& = & -8 \color{red}{+} (11+x) \\\Leftrightarrow & 4x-12& = &-8+11+x \\\Leftrightarrow & 4x \color{red}{-12} & = &3 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 4x-x& = &3+12 \\\Leftrightarrow & 3x& = &15 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{15}{ \color{red}{3} } \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-6x-2)& = & 2 \color{red}{-} (-3+x) \\\Leftrightarrow & -18x-6& = &2+3-x \\\Leftrightarrow & -18x \color{red}{-6} & = &5 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -18x+x& = &5+6 \\\Leftrightarrow & -17x& = &11 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{11}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-11}{17} & & \\ & V = \left\{ \frac{-11}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-3x-3)& = & 12 \color{red}{-} (3+x) \\\Leftrightarrow & -6x-6& = &12-3-x \\\Leftrightarrow & -6x \color{red}{-6} & = &9 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -6x+x& = &9+6 \\\Leftrightarrow & -5x& = &15 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{15}{ \color{red}{-5} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-3x-2)& = & 1 \color{red}{+} (15-2x) \\\Leftrightarrow & -9x-6& = &1+15-2x \\\Leftrightarrow & -9x \color{red}{-6} & = &16 \color{red}{-2x} \\\Leftrightarrow & -9x \color{red}{-6} \color{blue}{+6} \color{blue}{+2x} & = &16 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+6} \\\Leftrightarrow & -9x+2x& = &16+6 \\\Leftrightarrow & -7x& = &22 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{22}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-22}{7} & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (6x+5)& = & 5 \color{red}{+} (-7+x) \\\Leftrightarrow & 24x+20& = &5-7+x \\\Leftrightarrow & 24x \color{red}{+20} & = &-2 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 24x-x& = &-2-20 \\\Leftrightarrow & 23x& = &-22 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-22}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-22}{23} & & \\ & V = \left\{ \frac{-22}{23} \right\} & \\\end{align}\)