Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (5x+2)& = & -6 \color{red}{+} (8+3x) \\\Leftrightarrow & 10x+4& = &-6+8+3x \\\Leftrightarrow & 10x \color{red}{+4} & = &2 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+4} \color{blue}{-4} \color{blue}{-3x} & = &2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-4} \\\Leftrightarrow & 10x-3x& = &2-4 \\\Leftrightarrow & 7x& = &-2 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-2}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-2x-3)& = & 13 \color{red}{-} (-8+x) \\\Leftrightarrow & -10x-15& = &13+8-x \\\Leftrightarrow & -10x \color{red}{-15} & = &21 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -10x+x& = &21+15 \\\Leftrightarrow & -9x& = &36 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{36}{ \color{red}{-9} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-5x+1)& = & 6 \color{red}{+} (14+3x) \\\Leftrightarrow & -20x+4& = &6+14+3x \\\Leftrightarrow & -20x \color{red}{+4} & = &20 \color{red}{+3x} \\\Leftrightarrow & -20x \color{red}{+4} \color{blue}{-4} \color{blue}{-3x} & = &20 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-4} \\\Leftrightarrow & -20x-3x& = &20-4 \\\Leftrightarrow & -23x& = &16 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{16}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-16}{23} & & \\ & V = \left\{ \frac{-16}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (x+5)& = & 8 \color{red}{-} (-13+3x) \\\Leftrightarrow & 5x+25& = &8+13-3x \\\Leftrightarrow & 5x \color{red}{+25} & = &21 \color{red}{-3x} \\\Leftrightarrow & 5x \color{red}{+25} \color{blue}{-25} \color{blue}{+3x} & = &21 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-25} \\\Leftrightarrow & 5x+3x& = &21-25 \\\Leftrightarrow & 8x& = &-4 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{-4}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{-1}{2} & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (2x+5)& = & -5 \color{red}{+} (-5-5x) \\\Leftrightarrow & 6x+15& = &-5-5-5x \\\Leftrightarrow & 6x \color{red}{+15} & = &-10 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+15} \color{blue}{-15} \color{blue}{+5x} & = &-10 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-15} \\\Leftrightarrow & 6x+5x& = &-10-15 \\\Leftrightarrow & 11x& = &-25 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-25}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-25}{11} & & \\ & V = \left\{ \frac{-25}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (x+6)& = & 9 \color{red}{+} (-11-3x) \\\Leftrightarrow & 4x+24& = &9-11-3x \\\Leftrightarrow & 4x \color{red}{+24} & = &-2 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+24} \color{blue}{-24} \color{blue}{+3x} & = &-2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-24} \\\Leftrightarrow & 4x+3x& = &-2-24 \\\Leftrightarrow & 7x& = &-26 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-26}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-26}{7} & & \\ & V = \left\{ \frac{-26}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-4x+7)& = & -7 \color{red}{-} (-13+x) \\\Leftrightarrow & -12x+21& = &-7+13-x \\\Leftrightarrow & -12x \color{red}{+21} & = &6 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & -12x+x& = &6-21 \\\Leftrightarrow & -11x& = &-15 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-15}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{15}{11} & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-6x+4)& = & 4 \color{red}{-} (-7+x) \\\Leftrightarrow & -12x+8& = &4+7-x \\\Leftrightarrow & -12x \color{red}{+8} & = &11 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -12x+x& = &11-8 \\\Leftrightarrow & -11x& = &3 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{3}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-3}{11} & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (3x-4)& = & -12 \color{red}{-} (-15+x) \\\Leftrightarrow & 18x-24& = &-12+15-x \\\Leftrightarrow & 18x \color{red}{-24} & = &3 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 18x+x& = &3+24 \\\Leftrightarrow & 19x& = &27 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{27}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{27}{19} & & \\ & V = \left\{ \frac{27}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-2x+3)& = & -5 \color{red}{-} (-14+x) \\\Leftrightarrow & -6x+9& = &-5+14-x \\\Leftrightarrow & -6x \color{red}{+9} & = &9 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & -6x+x& = &9-9 \\\Leftrightarrow & -5x& = &0 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{0}{ \color{red}{-5} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (5x+2)& = & -2 \color{red}{-} (14+x) \\\Leftrightarrow & 20x+8& = &-2-14-x \\\Leftrightarrow & 20x \color{red}{+8} & = &-16 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 20x+x& = &-16-8 \\\Leftrightarrow & 21x& = &-24 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-24}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-8}{7} & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (3x+4)& = & -10 \color{red}{-} (7-5x) \\\Leftrightarrow & 6x+8& = &-10-7+5x \\\Leftrightarrow & 6x \color{red}{+8} & = &-17 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+8} \color{blue}{-8} \color{blue}{-5x} & = &-17 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-8} \\\Leftrightarrow & 6x-5x& = &-17-8 \\\Leftrightarrow & x& = &-25 \\ & V = \left\{ -25 \right\} & \\\end{align}\)