Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (2x+6)& = & -10 \color{red}{+} (-14+x) \\\Leftrightarrow & 12x+36& = &-10-14+x \\\Leftrightarrow & 12x \color{red}{+36} & = &-24 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &-24 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & 12x-x& = &-24-36 \\\Leftrightarrow & 11x& = &-60 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-60}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-60}{11} & & \\ & V = \left\{ \frac{-60}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-5x+1)& = & 4 \color{red}{+} (-11-3x) \\\Leftrightarrow & -10x+2& = &4-11-3x \\\Leftrightarrow & -10x \color{red}{+2} & = &-7 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+2} \color{blue}{-2} \color{blue}{+3x} & = &-7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-2} \\\Leftrightarrow & -10x+3x& = &-7-2 \\\Leftrightarrow & -7x& = &-9 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-9}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{9}{7} & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (x-1)& = & 13 \color{red}{-} (6+2x) \\\Leftrightarrow & 3x-3& = &13-6-2x \\\Leftrightarrow & 3x \color{red}{-3} & = &7 \color{red}{-2x} \\\Leftrightarrow & 3x \color{red}{-3} \color{blue}{+3} \color{blue}{+2x} & = &7 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+3} \\\Leftrightarrow & 3x+2x& = &7+3 \\\Leftrightarrow & 5x& = &10 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{10}{ \color{red}{5} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-4x-7)& = & 5 \color{red}{+} (-11+x) \\\Leftrightarrow & -12x-21& = &5-11+x \\\Leftrightarrow & -12x \color{red}{-21} & = &-6 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & -12x-x& = &-6+21 \\\Leftrightarrow & -13x& = &15 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{15}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-15}{13} & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (3x-7)& = & -2 \color{red}{-} (-15-4x) \\\Leftrightarrow & 9x-21& = &-2+15+4x \\\Leftrightarrow & 9x \color{red}{-21} & = &13 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{-21} \color{blue}{+21} \color{blue}{-4x} & = &13 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+21} \\\Leftrightarrow & 9x-4x& = &13+21 \\\Leftrightarrow & 5x& = &34 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{34}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{34}{5} & & \\ & V = \left\{ \frac{34}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-4x-6)& = & 8 \color{red}{-} (7+x) \\\Leftrightarrow & -12x-18& = &8-7-x \\\Leftrightarrow & -12x \color{red}{-18} & = &1 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -12x+x& = &1+18 \\\Leftrightarrow & -11x& = &19 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{19}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-19}{11} & & \\ & V = \left\{ \frac{-19}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (x+4)& = & 5 \color{red}{-} (-11+4x) \\\Leftrightarrow & 5x+20& = &5+11-4x \\\Leftrightarrow & 5x \color{red}{+20} & = &16 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{+20} \color{blue}{-20} \color{blue}{+4x} & = &16 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-20} \\\Leftrightarrow & 5x+4x& = &16-20 \\\Leftrightarrow & 9x& = &-4 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-4}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-4}{9} & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (2x-3)& = & 1 \color{red}{-} (-4+3x) \\\Leftrightarrow & 4x-6& = &1+4-3x \\\Leftrightarrow & 4x \color{red}{-6} & = &5 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-6} \color{blue}{+6} \color{blue}{+3x} & = &5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+6} \\\Leftrightarrow & 4x+3x& = &5+6 \\\Leftrightarrow & 7x& = &11 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{11}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{11}{7} & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (4x+4)& = & -7 \color{red}{-} (-10+x) \\\Leftrightarrow & 20x+20& = &-7+10-x \\\Leftrightarrow & 20x \color{red}{+20} & = &3 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 20x+x& = &3-20 \\\Leftrightarrow & 21x& = &-17 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-17}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-17}{21} & & \\ & V = \left\{ \frac{-17}{21} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-x-6)& = & 13 \color{red}{-} (-2-5x) \\\Leftrightarrow & -6x-36& = &13+2+5x \\\Leftrightarrow & -6x \color{red}{-36} & = &15 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-36} \color{blue}{+36} \color{blue}{-5x} & = &15 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+36} \\\Leftrightarrow & -6x-5x& = &15+36 \\\Leftrightarrow & -11x& = &51 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{51}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-51}{11} & & \\ & V = \left\{ \frac{-51}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (5x-5)& = & -7 \color{red}{+} (-7+x) \\\Leftrightarrow & 10x-10& = &-7-7+x \\\Leftrightarrow & 10x \color{red}{-10} & = &-14 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 10x-x& = &-14+10 \\\Leftrightarrow & 9x& = &-4 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-4}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-4}{9} & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (4x+2)& = & -1 \color{red}{+} (-5+x) \\\Leftrightarrow & 24x+12& = &-1-5+x \\\Leftrightarrow & 24x \color{red}{+12} & = &-6 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 24x-x& = &-6-12 \\\Leftrightarrow & 23x& = &-18 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-18}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-18}{23} & & \\ & V = \left\{ \frac{-18}{23} \right\} & \\\end{align}\)