Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (3x-1)& = & 11 \color{red}{-} (-5+x) \\\Leftrightarrow & 18x-6& = &11+5-x \\\Leftrightarrow & 18x \color{red}{-6} & = &16 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 18x+x& = &16+6 \\\Leftrightarrow & 19x& = &22 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{22}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{22}{19} & & \\ & V = \left\{ \frac{22}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (5x-2)& = & 9 \color{red}{+} (5-4x) \\\Leftrightarrow & 25x-10& = &9+5-4x \\\Leftrightarrow & 25x \color{red}{-10} & = &14 \color{red}{-4x} \\\Leftrightarrow & 25x \color{red}{-10} \color{blue}{+10} \color{blue}{+4x} & = &14 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+10} \\\Leftrightarrow & 25x+4x& = &14+10 \\\Leftrightarrow & 29x& = &24 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{24}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{24}{29} & & \\ & V = \left\{ \frac{24}{29} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (6x-2)& = & 3 \color{red}{-} (8-5x) \\\Leftrightarrow & 36x-12& = &3-8+5x \\\Leftrightarrow & 36x \color{red}{-12} & = &-5 \color{red}{+5x} \\\Leftrightarrow & 36x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &-5 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & 36x-5x& = &-5+12 \\\Leftrightarrow & 31x& = &7 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{7}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{7}{31} & & \\ & V = \left\{ \frac{7}{31} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (x+7)& = & -5 \color{red}{-} (-6-5x) \\\Leftrightarrow & 3x+21& = &-5+6+5x \\\Leftrightarrow & 3x \color{red}{+21} & = &1 \color{red}{+5x} \\\Leftrightarrow & 3x \color{red}{+21} \color{blue}{-21} \color{blue}{-5x} & = &1 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-21} \\\Leftrightarrow & 3x-5x& = &1-21 \\\Leftrightarrow & -2x& = &-20 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{-20}{ \color{red}{-2} } \\\Leftrightarrow & x = 10 & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-4x-1)& = & 5 \color{red}{+} (4+x) \\\Leftrightarrow & -8x-2& = &5+4+x \\\Leftrightarrow & -8x \color{red}{-2} & = &9 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & -8x-x& = &9+2 \\\Leftrightarrow & -9x& = &11 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{11}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-11}{9} & & \\ & V = \left\{ \frac{-11}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-x+3)& = & -13 \color{red}{+} (3-2x) \\\Leftrightarrow & -3x+9& = &-13+3-2x \\\Leftrightarrow & -3x \color{red}{+9} & = &-10 \color{red}{-2x} \\\Leftrightarrow & -3x \color{red}{+9} \color{blue}{-9} \color{blue}{+2x} & = &-10 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-9} \\\Leftrightarrow & -3x+2x& = &-10-9 \\\Leftrightarrow & -x& = &-19 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-19}{ \color{red}{-1} } \\\Leftrightarrow & x = 19 & & \\ & V = \left\{ 19 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-x+5)& = & 7 \color{red}{+} (-3+4x) \\\Leftrightarrow & -3x+15& = &7-3+4x \\\Leftrightarrow & -3x \color{red}{+15} & = &4 \color{red}{+4x} \\\Leftrightarrow & -3x \color{red}{+15} \color{blue}{-15} \color{blue}{-4x} & = &4 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-15} \\\Leftrightarrow & -3x-4x& = &4-15 \\\Leftrightarrow & -7x& = &-11 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-11}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{11}{7} & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (2x-2)& = & 13 \color{red}{-} (9+x) \\\Leftrightarrow & 8x-8& = &13-9-x \\\Leftrightarrow & 8x \color{red}{-8} & = &4 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 8x+x& = &4+8 \\\Leftrightarrow & 9x& = &12 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{12}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{4}{3} & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-4x+1)& = & -10 \color{red}{+} (-5+x) \\\Leftrightarrow & -8x+2& = &-10-5+x \\\Leftrightarrow & -8x \color{red}{+2} & = &-15 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+2} \color{blue}{-2} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{-2} \\\Leftrightarrow & -8x-x& = &-15-2 \\\Leftrightarrow & -9x& = &-17 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-17}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{17}{9} & & \\ & V = \left\{ \frac{17}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (3x+3)& = & -1 \color{red}{-} (-10-2x) \\\Leftrightarrow & 15x+15& = &-1+10+2x \\\Leftrightarrow & 15x \color{red}{+15} & = &9 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+15} \color{blue}{-15} \color{blue}{-2x} & = &9 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-15} \\\Leftrightarrow & 15x-2x& = &9-15 \\\Leftrightarrow & 13x& = &-6 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-6}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-6}{13} & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-6x-1)& = & -15 \color{red}{+} (3+x) \\\Leftrightarrow & -24x-4& = &-15+3+x \\\Leftrightarrow & -24x \color{red}{-4} & = &-12 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -24x-x& = &-12+4 \\\Leftrightarrow & -25x& = &-8 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-8}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{8}{25} & & \\ & V = \left\{ \frac{8}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (5x-6)& = & -5 \color{red}{-} (3+3x) \\\Leftrightarrow & 20x-24& = &-5-3-3x \\\Leftrightarrow & 20x \color{red}{-24} & = &-8 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{-24} \color{blue}{+24} \color{blue}{+3x} & = &-8 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+24} \\\Leftrightarrow & 20x+3x& = &-8+24 \\\Leftrightarrow & 23x& = &16 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{16}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{16}{23} & & \\ & V = \left\{ \frac{16}{23} \right\} & \\\end{align}\)