Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-5x+2)& = & -3 \color{red}{-} (-10+x) \\\Leftrightarrow & -30x+12& = &-3+10-x \\\Leftrightarrow & -30x \color{red}{+12} & = &7 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -30x+x& = &7-12 \\\Leftrightarrow & -29x& = &-5 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-5}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{5}{29} & & \\ & V = \left\{ \frac{5}{29} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (x+1)& = & -14 \color{red}{-} (-15+3x) \\\Leftrightarrow & 4x+4& = &-14+15-3x \\\Leftrightarrow & 4x \color{red}{+4} & = &1 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & 4x+3x& = &1-4 \\\Leftrightarrow & 7x& = &-3 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-3}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-3}{7} & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (3x+4)& = & 10 \color{red}{+} (-11+x) \\\Leftrightarrow & 9x+12& = &10-11+x \\\Leftrightarrow & 9x \color{red}{+12} & = &-1 \color{red}{+x} \\\Leftrightarrow & 9x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 9x-x& = &-1-12 \\\Leftrightarrow & 8x& = &-13 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{-13}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{-13}{8} & & \\ & V = \left\{ \frac{-13}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-3x-5)& = & -6 \color{red}{+} (5+x) \\\Leftrightarrow & -6x-10& = &-6+5+x \\\Leftrightarrow & -6x \color{red}{-10} & = &-1 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -6x-x& = &-1+10 \\\Leftrightarrow & -7x& = &9 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{9}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-9}{7} & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (x+4)& = & 9 \color{red}{+} (14+x) \\\Leftrightarrow & 5x+20& = &9+14+x \\\Leftrightarrow & 5x \color{red}{+20} & = &23 \color{red}{+x} \\\Leftrightarrow & 5x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &23 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 5x-x& = &23-20 \\\Leftrightarrow & 4x& = &3 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{3}{ \color{red}{4} } \\\Leftrightarrow & x = \frac{3}{4} & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-4x-3)& = & -6 \color{red}{-} (2+3x) \\\Leftrightarrow & -16x-12& = &-6-2-3x \\\Leftrightarrow & -16x \color{red}{-12} & = &-8 \color{red}{-3x} \\\Leftrightarrow & -16x \color{red}{-12} \color{blue}{+12} \color{blue}{+3x} & = &-8 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+12} \\\Leftrightarrow & -16x+3x& = &-8+12 \\\Leftrightarrow & -13x& = &4 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{4}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-4}{13} & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (x+1)& = & -14 \color{red}{-} (15+4x) \\\Leftrightarrow & 3x+3& = &-14-15-4x \\\Leftrightarrow & 3x \color{red}{+3} & = &-29 \color{red}{-4x} \\\Leftrightarrow & 3x \color{red}{+3} \color{blue}{-3} \color{blue}{+4x} & = &-29 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-3} \\\Leftrightarrow & 3x+4x& = &-29-3 \\\Leftrightarrow & 7x& = &-32 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-32}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-32}{7} & & \\ & V = \left\{ \frac{-32}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (4x+7)& = & 13 \color{red}{+} (7-5x) \\\Leftrightarrow & 8x+14& = &13+7-5x \\\Leftrightarrow & 8x \color{red}{+14} & = &20 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{+14} \color{blue}{-14} \color{blue}{+5x} & = &20 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-14} \\\Leftrightarrow & 8x+5x& = &20-14 \\\Leftrightarrow & 13x& = &6 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{6}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{6}{13} & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (6x-5)& = & 13 \color{red}{-} (13+x) \\\Leftrightarrow & 36x-30& = &13-13-x \\\Leftrightarrow & 36x \color{red}{-30} & = &0 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 36x+x& = &0+30 \\\Leftrightarrow & 37x& = &30 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{30}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{30}{37} & & \\ & V = \left\{ \frac{30}{37} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-x+3)& = & -13 \color{red}{+} (9+x) \\\Leftrightarrow & -6x+18& = &-13+9+x \\\Leftrightarrow & -6x \color{red}{+18} & = &-4 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -6x-x& = &-4-18 \\\Leftrightarrow & -7x& = &-22 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-22}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{22}{7} & & \\ & V = \left\{ \frac{22}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (2x+1)& = & 2 \color{red}{+} (-9-5x) \\\Leftrightarrow & 6x+3& = &2-9-5x \\\Leftrightarrow & 6x \color{red}{+3} & = &-7 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+3} \color{blue}{-3} \color{blue}{+5x} & = &-7 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-3} \\\Leftrightarrow & 6x+5x& = &-7-3 \\\Leftrightarrow & 11x& = &-10 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-10}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-10}{11} & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-6x-6)& = & -10 \color{red}{-} (-7-5x) \\\Leftrightarrow & -36x-36& = &-10+7+5x \\\Leftrightarrow & -36x \color{red}{-36} & = &-3 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{-36} \color{blue}{+36} \color{blue}{-5x} & = &-3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+36} \\\Leftrightarrow & -36x-5x& = &-3+36 \\\Leftrightarrow & -41x& = &33 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{33}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{-33}{41} & & \\ & V = \left\{ \frac{-33}{41} \right\} & \\\end{align}\)