Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-3x-2)& = & -7 \color{red}{+} (-10+x) \\\Leftrightarrow & -6x-4& = &-7-10+x \\\Leftrightarrow & -6x \color{red}{-4} & = &-17 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -6x-x& = &-17+4 \\\Leftrightarrow & -7x& = &-13 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-13}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{13}{7} & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (5x+2)& = & -6 \color{red}{-} (-8-3x) \\\Leftrightarrow & 10x+4& = &-6+8+3x \\\Leftrightarrow & 10x \color{red}{+4} & = &2 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+4} \color{blue}{-4} \color{blue}{-3x} & = &2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-4} \\\Leftrightarrow & 10x-3x& = &2-4 \\\Leftrightarrow & 7x& = &-2 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-2}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-4x+1)& = & -15 \color{red}{-} (15-5x) \\\Leftrightarrow & -16x+4& = &-15-15+5x \\\Leftrightarrow & -16x \color{red}{+4} & = &-30 \color{red}{+5x} \\\Leftrightarrow & -16x \color{red}{+4} \color{blue}{-4} \color{blue}{-5x} & = &-30 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-4} \\\Leftrightarrow & -16x-5x& = &-30-4 \\\Leftrightarrow & -21x& = &-34 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-34}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{34}{21} & & \\ & V = \left\{ \frac{34}{21} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-6x-6)& = & -12 \color{red}{-} (-12+x) \\\Leftrightarrow & -24x-24& = &-12+12-x \\\Leftrightarrow & -24x \color{red}{-24} & = &0 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -24x+x& = &0+24 \\\Leftrightarrow & -23x& = &24 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{24}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-24}{23} & & \\ & V = \left\{ \frac{-24}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-x-4)& = & 10 \color{red}{+} (8+2x) \\\Leftrightarrow & -3x-12& = &10+8+2x \\\Leftrightarrow & -3x \color{red}{-12} & = &18 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{-12} \color{blue}{+12} \color{blue}{-2x} & = &18 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+12} \\\Leftrightarrow & -3x-2x& = &18+12 \\\Leftrightarrow & -5x& = &30 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{30}{ \color{red}{-5} } \\\Leftrightarrow & x = -6 & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (4x+2)& = & 7 \color{red}{-} (-15+x) \\\Leftrightarrow & 12x+6& = &7+15-x \\\Leftrightarrow & 12x \color{red}{+6} & = &22 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &22 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 12x+x& = &22-6 \\\Leftrightarrow & 13x& = &16 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{16}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{16}{13} & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-2x+2)& = & 11 \color{red}{-} (-3+x) \\\Leftrightarrow & -12x+12& = &11+3-x \\\Leftrightarrow & -12x \color{red}{+12} & = &14 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -12x+x& = &14-12 \\\Leftrightarrow & -11x& = &2 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{2}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-2}{11} & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-x+6)& = & -8 \color{red}{-} (8+3x) \\\Leftrightarrow & -4x+24& = &-8-8-3x \\\Leftrightarrow & -4x \color{red}{+24} & = &-16 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+24} \color{blue}{-24} \color{blue}{+3x} & = &-16 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-24} \\\Leftrightarrow & -4x+3x& = &-16-24 \\\Leftrightarrow & -x& = &-40 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-40}{ \color{red}{-1} } \\\Leftrightarrow & x = 40 & & \\ & V = \left\{ 40 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-6x+3)& = & 11 \color{red}{-} (7+x) \\\Leftrightarrow & -30x+15& = &11-7-x \\\Leftrightarrow & -30x \color{red}{+15} & = &4 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -30x+x& = &4-15 \\\Leftrightarrow & -29x& = &-11 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-11}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{11}{29} & & \\ & V = \left\{ \frac{11}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-4x+3)& = & 7 \color{red}{-} (-14+x) \\\Leftrightarrow & -20x+15& = &7+14-x \\\Leftrightarrow & -20x \color{red}{+15} & = &21 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -20x+x& = &21-15 \\\Leftrightarrow & -19x& = &6 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{6}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-6}{19} & & \\ & V = \left\{ \frac{-6}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (x-3)& = & -6 \color{red}{-} (11-5x) \\\Leftrightarrow & 6x-18& = &-6-11+5x \\\Leftrightarrow & 6x \color{red}{-18} & = &-17 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-18} \color{blue}{+18} \color{blue}{-5x} & = &-17 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+18} \\\Leftrightarrow & 6x-5x& = &-17+18 \\\Leftrightarrow & x& = &1 \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-3x-7)& = & -7 \color{red}{-} (-2+x) \\\Leftrightarrow & -6x-14& = &-7+2-x \\\Leftrightarrow & -6x \color{red}{-14} & = &-5 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & -6x+x& = &-5+14 \\\Leftrightarrow & -5x& = &9 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{9}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-9}{5} & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)