Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (6x-1)& = & 15 \color{red}{-} (-2+x) \\\Leftrightarrow & 12x-2& = &15+2-x \\\Leftrightarrow & 12x \color{red}{-2} & = &17 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & 12x+x& = &17+2 \\\Leftrightarrow & 13x& = &19 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{19}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{19}{13} & & \\ & V = \left\{ \frac{19}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-6x+7)& = & 1 \color{red}{-} (1+x) \\\Leftrightarrow & -18x+21& = &1-1-x \\\Leftrightarrow & -18x \color{red}{+21} & = &0 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & -18x+x& = &0-21 \\\Leftrightarrow & -17x& = &-21 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-21}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{21}{17} & & \\ & V = \left\{ \frac{21}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-x-1)& = & 9 \color{red}{-} (13+x) \\\Leftrightarrow & -4x-4& = &9-13-x \\\Leftrightarrow & -4x \color{red}{-4} & = &-4 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -4x+x& = &-4+4 \\\Leftrightarrow & -3x& = &0 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{0}{ \color{red}{-3} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (3x+1)& = & 5 \color{red}{+} (14+x) \\\Leftrightarrow & 12x+4& = &5+14+x \\\Leftrightarrow & 12x \color{red}{+4} & = &19 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 12x-x& = &19-4 \\\Leftrightarrow & 11x& = &15 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{15}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{15}{11} & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (x+2)& = & -3 \color{red}{-} (5-2x) \\\Leftrightarrow & 3x+6& = &-3-5+2x \\\Leftrightarrow & 3x \color{red}{+6} & = &-8 \color{red}{+2x} \\\Leftrightarrow & 3x \color{red}{+6} \color{blue}{-6} \color{blue}{-2x} & = &-8 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-6} \\\Leftrightarrow & 3x-2x& = &-8-6 \\\Leftrightarrow & x& = &-14 \\ & V = \left\{ -14 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-5x+2)& = & -9 \color{red}{-} (13-2x) \\\Leftrightarrow & -15x+6& = &-9-13+2x \\\Leftrightarrow & -15x \color{red}{+6} & = &-22 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+6} \color{blue}{-6} \color{blue}{-2x} & = &-22 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-6} \\\Leftrightarrow & -15x-2x& = &-22-6 \\\Leftrightarrow & -17x& = &-28 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-28}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{28}{17} & & \\ & V = \left\{ \frac{28}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (6x-6)& = & 12 \color{red}{+} (-10-5x) \\\Leftrightarrow & 18x-18& = &12-10-5x \\\Leftrightarrow & 18x \color{red}{-18} & = &2 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-18} \color{blue}{+18} \color{blue}{+5x} & = &2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+18} \\\Leftrightarrow & 18x+5x& = &2+18 \\\Leftrightarrow & 23x& = &20 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{20}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{20}{23} & & \\ & V = \left\{ \frac{20}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-2x+6)& = & -8 \color{red}{-} (-2+x) \\\Leftrightarrow & -12x+36& = &-8+2-x \\\Leftrightarrow & -12x \color{red}{+36} & = &-6 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & -12x+x& = &-6-36 \\\Leftrightarrow & -11x& = &-42 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-42}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{42}{11} & & \\ & V = \left\{ \frac{42}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-4x-1)& = & -6 \color{red}{-} (6+x) \\\Leftrightarrow & -8x-2& = &-6-6-x \\\Leftrightarrow & -8x \color{red}{-2} & = &-12 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & -8x+x& = &-12+2 \\\Leftrightarrow & -7x& = &-10 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-10}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{10}{7} & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-x-1)& = & -4 \color{red}{-} (5-4x) \\\Leftrightarrow & -5x-5& = &-4-5+4x \\\Leftrightarrow & -5x \color{red}{-5} & = &-9 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{-5} \color{blue}{+5} \color{blue}{-4x} & = &-9 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+5} \\\Leftrightarrow & -5x-4x& = &-9+5 \\\Leftrightarrow & -9x& = &-4 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-4}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{4}{9} & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-5x+2)& = & 5 \color{red}{+} (-3+3x) \\\Leftrightarrow & -10x+4& = &5-3+3x \\\Leftrightarrow & -10x \color{red}{+4} & = &2 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+4} \color{blue}{-4} \color{blue}{-3x} & = &2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-4} \\\Leftrightarrow & -10x-3x& = &2-4 \\\Leftrightarrow & -13x& = &-2 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-2}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{2}{13} & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (6x-1)& = & -6 \color{red}{-} (-9-5x) \\\Leftrightarrow & 18x-3& = &-6+9+5x \\\Leftrightarrow & 18x \color{red}{-3} & = &3 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-3} \color{blue}{+3} \color{blue}{-5x} & = &3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+3} \\\Leftrightarrow & 18x-5x& = &3+3 \\\Leftrightarrow & 13x& = &6 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{6}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{6}{13} & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)