Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-x-5)& = & 4 \color{red}{-} (-9+x) \\\Leftrightarrow & -2x-10& = &4+9-x \\\Leftrightarrow & -2x \color{red}{-10} & = &13 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -2x+x& = &13+10 \\\Leftrightarrow & -x& = &23 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{23}{ \color{red}{-1} } \\\Leftrightarrow & x = -23 & & \\ & V = \left\{ -23 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-3x+6)& = & -9 \color{red}{+} (10-2x) \\\Leftrightarrow & -15x+30& = &-9+10-2x \\\Leftrightarrow & -15x \color{red}{+30} & = &1 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+30} \color{blue}{-30} \color{blue}{+2x} & = &1 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-30} \\\Leftrightarrow & -15x+2x& = &1-30 \\\Leftrightarrow & -13x& = &-29 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-29}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{29}{13} & & \\ & V = \left\{ \frac{29}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (4x-7)& = & -15 \color{red}{+} (-1+x) \\\Leftrightarrow & 12x-21& = &-15-1+x \\\Leftrightarrow & 12x \color{red}{-21} & = &-16 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & 12x-x& = &-16+21 \\\Leftrightarrow & 11x& = &5 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{5}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{5}{11} & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (2x+7)& = & 15 \color{red}{-} (4+x) \\\Leftrightarrow & 4x+14& = &15-4-x \\\Leftrightarrow & 4x \color{red}{+14} & = &11 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & 4x+x& = &11-14 \\\Leftrightarrow & 5x& = &-3 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-3}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-3}{5} & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-x+1)& = & 2 \color{red}{-} (-6-2x) \\\Leftrightarrow & -5x+5& = &2+6+2x \\\Leftrightarrow & -5x \color{red}{+5} & = &8 \color{red}{+2x} \\\Leftrightarrow & -5x \color{red}{+5} \color{blue}{-5} \color{blue}{-2x} & = &8 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-5} \\\Leftrightarrow & -5x-2x& = &8-5 \\\Leftrightarrow & -7x& = &3 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{3}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-3}{7} & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (2x-4)& = & 11 \color{red}{+} (8-3x) \\\Leftrightarrow & 10x-20& = &11+8-3x \\\Leftrightarrow & 10x \color{red}{-20} & = &19 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-20} \color{blue}{+20} \color{blue}{+3x} & = &19 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+20} \\\Leftrightarrow & 10x+3x& = &19+20 \\\Leftrightarrow & 13x& = &39 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{39}{ \color{red}{13} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (x-3)& = & -12 \color{red}{+} (-12-2x) \\\Leftrightarrow & 5x-15& = &-12-12-2x \\\Leftrightarrow & 5x \color{red}{-15} & = &-24 \color{red}{-2x} \\\Leftrightarrow & 5x \color{red}{-15} \color{blue}{+15} \color{blue}{+2x} & = &-24 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+15} \\\Leftrightarrow & 5x+2x& = &-24+15 \\\Leftrightarrow & 7x& = &-9 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-9}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-9}{7} & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-3x-1)& = & -2 \color{red}{-} (-4+x) \\\Leftrightarrow & -6x-2& = &-2+4-x \\\Leftrightarrow & -6x \color{red}{-2} & = &2 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & -6x+x& = &2+2 \\\Leftrightarrow & -5x& = &4 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{4}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-4}{5} & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (6x+1)& = & 11 \color{red}{-} (-9+x) \\\Leftrightarrow & 36x+6& = &11+9-x \\\Leftrightarrow & 36x \color{red}{+6} & = &20 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 36x+x& = &20-6 \\\Leftrightarrow & 37x& = &14 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{14}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{14}{37} & & \\ & V = \left\{ \frac{14}{37} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (x+5)& = & 8 \color{red}{+} (-1-5x) \\\Leftrightarrow & 3x+15& = &8-1-5x \\\Leftrightarrow & 3x \color{red}{+15} & = &7 \color{red}{-5x} \\\Leftrightarrow & 3x \color{red}{+15} \color{blue}{-15} \color{blue}{+5x} & = &7 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-15} \\\Leftrightarrow & 3x+5x& = &7-15 \\\Leftrightarrow & 8x& = &-8 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{-8}{ \color{red}{8} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-x-3)& = & 14 \color{red}{+} (-5+x) \\\Leftrightarrow & -4x-12& = &14-5+x \\\Leftrightarrow & -4x \color{red}{-12} & = &9 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -4x-x& = &9+12 \\\Leftrightarrow & -5x& = &21 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{21}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-21}{5} & & \\ & V = \left\{ \frac{-21}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-4x-1)& = & -11 \color{red}{+} (-7-5x) \\\Leftrightarrow & -16x-4& = &-11-7-5x \\\Leftrightarrow & -16x \color{red}{-4} & = &-18 \color{red}{-5x} \\\Leftrightarrow & -16x \color{red}{-4} \color{blue}{+4} \color{blue}{+5x} & = &-18 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+4} \\\Leftrightarrow & -16x+5x& = &-18+4 \\\Leftrightarrow & -11x& = &-14 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-14}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{14}{11} & & \\ & V = \left\{ \frac{14}{11} \right\} & \\\end{align}\)