Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (3x+4)& = & -3 \color{red}{-} (-8+4x) \\\Leftrightarrow & 9x+12& = &-3+8-4x \\\Leftrightarrow & 9x \color{red}{+12} & = &5 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{+12} \color{blue}{-12} \color{blue}{+4x} & = &5 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-12} \\\Leftrightarrow & 9x+4x& = &5-12 \\\Leftrightarrow & 13x& = &-7 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-7}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-7}{13} & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-6x-7)& = & -1 \color{red}{-} (-5+x) \\\Leftrightarrow & -18x-21& = &-1+5-x \\\Leftrightarrow & -18x \color{red}{-21} & = &4 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-21} \color{blue}{+21} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+21} \\\Leftrightarrow & -18x+x& = &4+21 \\\Leftrightarrow & -17x& = &25 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{25}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-25}{17} & & \\ & V = \left\{ \frac{-25}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-x-2)& = & -3 \color{red}{+} (-7+x) \\\Leftrightarrow & -6x-12& = &-3-7+x \\\Leftrightarrow & -6x \color{red}{-12} & = &-10 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -6x-x& = &-10+12 \\\Leftrightarrow & -7x& = &2 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{2}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-2x-4)& = & 1 \color{red}{-} (11-3x) \\\Leftrightarrow & -4x-8& = &1-11+3x \\\Leftrightarrow & -4x \color{red}{-8} & = &-10 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &-10 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & -4x-3x& = &-10+8 \\\Leftrightarrow & -7x& = &-2 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-2}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-2x+5)& = & -10 \color{red}{-} (6+x) \\\Leftrightarrow & -12x+30& = &-10-6-x \\\Leftrightarrow & -12x \color{red}{+30} & = &-16 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -12x+x& = &-16-30 \\\Leftrightarrow & -11x& = &-46 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-46}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{46}{11} & & \\ & V = \left\{ \frac{46}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-5x+3)& = & 11 \color{red}{+} (-8+x) \\\Leftrightarrow & -30x+18& = &11-8+x \\\Leftrightarrow & -30x \color{red}{+18} & = &3 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -30x-x& = &3-18 \\\Leftrightarrow & -31x& = &-15 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-15}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{15}{31} & & \\ & V = \left\{ \frac{15}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-x+2)& = & -9 \color{red}{-} (6+x) \\\Leftrightarrow & -3x+6& = &-9-6-x \\\Leftrightarrow & -3x \color{red}{+6} & = &-15 \color{red}{-x} \\\Leftrightarrow & -3x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -3x+x& = &-15-6 \\\Leftrightarrow & -2x& = &-21 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{-21}{ \color{red}{-2} } \\\Leftrightarrow & x = \frac{21}{2} & & \\ & V = \left\{ \frac{21}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (4x+2)& = & 12 \color{red}{-} (5+x) \\\Leftrightarrow & 8x+4& = &12-5-x \\\Leftrightarrow & 8x \color{red}{+4} & = &7 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 8x+x& = &7-4 \\\Leftrightarrow & 9x& = &3 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{3}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{1}{3} & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (5x+3)& = & 9 \color{red}{-} (8-3x) \\\Leftrightarrow & 25x+15& = &9-8+3x \\\Leftrightarrow & 25x \color{red}{+15} & = &1 \color{red}{+3x} \\\Leftrightarrow & 25x \color{red}{+15} \color{blue}{-15} \color{blue}{-3x} & = &1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-15} \\\Leftrightarrow & 25x-3x& = &1-15 \\\Leftrightarrow & 22x& = &-14 \\\Leftrightarrow & \frac{22x}{ \color{red}{22} }& = &\frac{-14}{ \color{red}{22} } \\\Leftrightarrow & x = \frac{-7}{11} & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-6x-1)& = & -3 \color{red}{+} (-14-5x) \\\Leftrightarrow & -36x-6& = &-3-14-5x \\\Leftrightarrow & -36x \color{red}{-6} & = &-17 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &-17 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & -36x+5x& = &-17+6 \\\Leftrightarrow & -31x& = &-11 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-11}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{11}{31} & & \\ & V = \left\{ \frac{11}{31} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (2x-7)& = & 13 \color{red}{+} (-8-3x) \\\Leftrightarrow & 4x-14& = &13-8-3x \\\Leftrightarrow & 4x \color{red}{-14} & = &5 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-14} \color{blue}{+14} \color{blue}{+3x} & = &5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+14} \\\Leftrightarrow & 4x+3x& = &5+14 \\\Leftrightarrow & 7x& = &19 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{19}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{19}{7} & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-2x+7)& = & 6 \color{red}{+} (13+3x) \\\Leftrightarrow & -10x+35& = &6+13+3x \\\Leftrightarrow & -10x \color{red}{+35} & = &19 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+35} \color{blue}{-35} \color{blue}{-3x} & = &19 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-35} \\\Leftrightarrow & -10x-3x& = &19-35 \\\Leftrightarrow & -13x& = &-16 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-16}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{16}{13} & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)