Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-3x+3)& = & -5 \color{red}{-} (4-2x) \\\Leftrightarrow & -9x+9& = &-5-4+2x \\\Leftrightarrow & -9x \color{red}{+9} & = &-9 \color{red}{+2x} \\\Leftrightarrow & -9x \color{red}{+9} \color{blue}{-9} \color{blue}{-2x} & = &-9 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-9} \\\Leftrightarrow & -9x-2x& = &-9-9 \\\Leftrightarrow & -11x& = &-18 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-18}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{18}{11} & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (3x+2)& = & -14 \color{red}{+} (12-2x) \\\Leftrightarrow & 9x+6& = &-14+12-2x \\\Leftrightarrow & 9x \color{red}{+6} & = &-2 \color{red}{-2x} \\\Leftrightarrow & 9x \color{red}{+6} \color{blue}{-6} \color{blue}{+2x} & = &-2 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-6} \\\Leftrightarrow & 9x+2x& = &-2-6 \\\Leftrightarrow & 11x& = &-8 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-8}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-8}{11} & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (3x+5)& = & 15 \color{red}{+} (-3-2x) \\\Leftrightarrow & 9x+15& = &15-3-2x \\\Leftrightarrow & 9x \color{red}{+15} & = &12 \color{red}{-2x} \\\Leftrightarrow & 9x \color{red}{+15} \color{blue}{-15} \color{blue}{+2x} & = &12 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-15} \\\Leftrightarrow & 9x+2x& = &12-15 \\\Leftrightarrow & 11x& = &-3 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-3}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-3}{11} & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (3x-2)& = & 5 \color{red}{+} (-8+x) \\\Leftrightarrow & 18x-12& = &5-8+x \\\Leftrightarrow & 18x \color{red}{-12} & = &-3 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 18x-x& = &-3+12 \\\Leftrightarrow & 17x& = &9 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{9}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{9}{17} & & \\ & V = \left\{ \frac{9}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-6x-7)& = & 2 \color{red}{-} (-10+x) \\\Leftrightarrow & -18x-21& = &2+10-x \\\Leftrightarrow & -18x \color{red}{-21} & = &12 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-21} \color{blue}{+21} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{+21} \\\Leftrightarrow & -18x+x& = &12+21 \\\Leftrightarrow & -17x& = &33 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{33}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-33}{17} & & \\ & V = \left\{ \frac{-33}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (2x-5)& = & 13 \color{red}{-} (5-5x) \\\Leftrightarrow & 8x-20& = &13-5+5x \\\Leftrightarrow & 8x \color{red}{-20} & = &8 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{-20} \color{blue}{+20} \color{blue}{-5x} & = &8 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+20} \\\Leftrightarrow & 8x-5x& = &8+20 \\\Leftrightarrow & 3x& = &28 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{28}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{28}{3} & & \\ & V = \left\{ \frac{28}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (2x-6)& = & -1 \color{red}{-} (-10+3x) \\\Leftrightarrow & 8x-24& = &-1+10-3x \\\Leftrightarrow & 8x \color{red}{-24} & = &9 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{-24} \color{blue}{+24} \color{blue}{+3x} & = &9 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+24} \\\Leftrightarrow & 8x+3x& = &9+24 \\\Leftrightarrow & 11x& = &33 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{33}{ \color{red}{11} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (6x+7)& = & -9 \color{red}{+} (-1+x) \\\Leftrightarrow & 24x+28& = &-9-1+x \\\Leftrightarrow & 24x \color{red}{+28} & = &-10 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & 24x-x& = &-10-28 \\\Leftrightarrow & 23x& = &-38 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-38}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-38}{23} & & \\ & V = \left\{ \frac{-38}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-3x+6)& = & 4 \color{red}{-} (-5+x) \\\Leftrightarrow & -6x+12& = &4+5-x \\\Leftrightarrow & -6x \color{red}{+12} & = &9 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -6x+x& = &9-12 \\\Leftrightarrow & -5x& = &-3 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-3}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{3}{5} & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (5x+5)& = & 3 \color{red}{-} (4-2x) \\\Leftrightarrow & 25x+25& = &3-4+2x \\\Leftrightarrow & 25x \color{red}{+25} & = &-1 \color{red}{+2x} \\\Leftrightarrow & 25x \color{red}{+25} \color{blue}{-25} \color{blue}{-2x} & = &-1 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-25} \\\Leftrightarrow & 25x-2x& = &-1-25 \\\Leftrightarrow & 23x& = &-26 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-26}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-26}{23} & & \\ & V = \left\{ \frac{-26}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-4x-6)& = & -5 \color{red}{-} (-4+x) \\\Leftrightarrow & -16x-24& = &-5+4-x \\\Leftrightarrow & -16x \color{red}{-24} & = &-1 \color{red}{-x} \\\Leftrightarrow & -16x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -16x+x& = &-1+24 \\\Leftrightarrow & -15x& = &23 \\\Leftrightarrow & \frac{-15x}{ \color{red}{-15} }& = &\frac{23}{ \color{red}{-15} } \\\Leftrightarrow & x = \frac{-23}{15} & & \\ & V = \left\{ \frac{-23}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (3x-3)& = & 14 \color{red}{+} (-9-5x) \\\Leftrightarrow & 18x-18& = &14-9-5x \\\Leftrightarrow & 18x \color{red}{-18} & = &5 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-18} \color{blue}{+18} \color{blue}{+5x} & = &5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+18} \\\Leftrightarrow & 18x+5x& = &5+18 \\\Leftrightarrow & 23x& = &23 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{23}{ \color{red}{23} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)