Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (5x+1)& = & -7 \color{red}{-} (-8+x) \\\Leftrightarrow & 20x+4& = &-7+8-x \\\Leftrightarrow & 20x \color{red}{+4} & = &1 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 20x+x& = &1-4 \\\Leftrightarrow & 21x& = &-3 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-3}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (3x+2)& = & -10 \color{red}{-} (3+x) \\\Leftrightarrow & 6x+4& = &-10-3-x \\\Leftrightarrow & 6x \color{red}{+4} & = &-13 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 6x+x& = &-13-4 \\\Leftrightarrow & 7x& = &-17 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-17}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-17}{7} & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-x-5)& = & 2 \color{red}{-} (4+3x) \\\Leftrightarrow & -2x-10& = &2-4-3x \\\Leftrightarrow & -2x \color{red}{-10} & = &-2 \color{red}{-3x} \\\Leftrightarrow & -2x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &-2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & -2x+3x& = &-2+10 \\\Leftrightarrow & x& = &8 \\ & V = \left\{ 8 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-x+5)& = & -6 \color{red}{+} (-9+4x) \\\Leftrightarrow & -3x+15& = &-6-9+4x \\\Leftrightarrow & -3x \color{red}{+15} & = &-15 \color{red}{+4x} \\\Leftrightarrow & -3x \color{red}{+15} \color{blue}{-15} \color{blue}{-4x} & = &-15 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-15} \\\Leftrightarrow & -3x-4x& = &-15-15 \\\Leftrightarrow & -7x& = &-30 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-30}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{30}{7} & & \\ & V = \left\{ \frac{30}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-2x+3)& = & -2 \color{red}{+} (4+x) \\\Leftrightarrow & -12x+18& = &-2+4+x \\\Leftrightarrow & -12x \color{red}{+18} & = &2 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -12x-x& = &2-18 \\\Leftrightarrow & -13x& = &-16 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-16}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{16}{13} & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-4x+5)& = & 5 \color{red}{+} (-5+x) \\\Leftrightarrow & -24x+30& = &5-5+x \\\Leftrightarrow & -24x \color{red}{+30} & = &0 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -24x-x& = &0-30 \\\Leftrightarrow & -25x& = &-30 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-30}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{6}{5} & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (6x+6)& = & 9 \color{red}{-} (15+x) \\\Leftrightarrow & 30x+30& = &9-15-x \\\Leftrightarrow & 30x \color{red}{+30} & = &-6 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 30x+x& = &-6-30 \\\Leftrightarrow & 31x& = &-36 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-36}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-36}{31} & & \\ & V = \left\{ \frac{-36}{31} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-4x+6)& = & -10 \color{red}{-} (4+x) \\\Leftrightarrow & -12x+18& = &-10-4-x \\\Leftrightarrow & -12x \color{red}{+18} & = &-14 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -12x+x& = &-14-18 \\\Leftrightarrow & -11x& = &-32 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-32}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{32}{11} & & \\ & V = \left\{ \frac{32}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (3x-6)& = & 3 \color{red}{+} (-5-2x) \\\Leftrightarrow & 9x-18& = &3-5-2x \\\Leftrightarrow & 9x \color{red}{-18} & = &-2 \color{red}{-2x} \\\Leftrightarrow & 9x \color{red}{-18} \color{blue}{+18} \color{blue}{+2x} & = &-2 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+18} \\\Leftrightarrow & 9x+2x& = &-2+18 \\\Leftrightarrow & 11x& = &16 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{16}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{16}{11} & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (4x+6)& = & -2 \color{red}{-} (14+x) \\\Leftrightarrow & 12x+18& = &-2-14-x \\\Leftrightarrow & 12x \color{red}{+18} & = &-16 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 12x+x& = &-16-18 \\\Leftrightarrow & 13x& = &-34 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-34}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-34}{13} & & \\ & V = \left\{ \frac{-34}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-4x+4)& = & -14 \color{red}{+} (3-3x) \\\Leftrightarrow & -16x+16& = &-14+3-3x \\\Leftrightarrow & -16x \color{red}{+16} & = &-11 \color{red}{-3x} \\\Leftrightarrow & -16x \color{red}{+16} \color{blue}{-16} \color{blue}{+3x} & = &-11 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-16} \\\Leftrightarrow & -16x+3x& = &-11-16 \\\Leftrightarrow & -13x& = &-27 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-27}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{27}{13} & & \\ & V = \left\{ \frac{27}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-5x+1)& = & -7 \color{red}{+} (-9+3x) \\\Leftrightarrow & -10x+2& = &-7-9+3x \\\Leftrightarrow & -10x \color{red}{+2} & = &-16 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+2} \color{blue}{-2} \color{blue}{-3x} & = &-16 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-2} \\\Leftrightarrow & -10x-3x& = &-16-2 \\\Leftrightarrow & -13x& = &-18 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-18}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{18}{13} & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)