Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-2x+2)& = & -4 \color{red}{+} (-8+3x) \\\Leftrightarrow & -8x+8& = &-4-8+3x \\\Leftrightarrow & -8x \color{red}{+8} & = &-12 \color{red}{+3x} \\\Leftrightarrow & -8x \color{red}{+8} \color{blue}{-8} \color{blue}{-3x} & = &-12 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-8} \\\Leftrightarrow & -8x-3x& = &-12-8 \\\Leftrightarrow & -11x& = &-20 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-20}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{20}{11} & & \\ & V = \left\{ \frac{20}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (5x-6)& = & -5 \color{red}{+} (3-4x) \\\Leftrightarrow & 25x-30& = &-5+3-4x \\\Leftrightarrow & 25x \color{red}{-30} & = &-2 \color{red}{-4x} \\\Leftrightarrow & 25x \color{red}{-30} \color{blue}{+30} \color{blue}{+4x} & = &-2 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+30} \\\Leftrightarrow & 25x+4x& = &-2+30 \\\Leftrightarrow & 29x& = &28 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{28}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{28}{29} & & \\ & V = \left\{ \frac{28}{29} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-6x+5)& = & 7 \color{red}{-} (11+x) \\\Leftrightarrow & -24x+20& = &7-11-x \\\Leftrightarrow & -24x \color{red}{+20} & = &-4 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -24x+x& = &-4-20 \\\Leftrightarrow & -23x& = &-24 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-24}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{24}{23} & & \\ & V = \left\{ \frac{24}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-5x+2)& = & 15 \color{red}{+} (11+4x) \\\Leftrightarrow & -25x+10& = &15+11+4x \\\Leftrightarrow & -25x \color{red}{+10} & = &26 \color{red}{+4x} \\\Leftrightarrow & -25x \color{red}{+10} \color{blue}{-10} \color{blue}{-4x} & = &26 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-10} \\\Leftrightarrow & -25x-4x& = &26-10 \\\Leftrightarrow & -29x& = &16 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{16}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-16}{29} & & \\ & V = \left\{ \frac{-16}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (5x-1)& = & 11 \color{red}{+} (9+x) \\\Leftrightarrow & 10x-2& = &11+9+x \\\Leftrightarrow & 10x \color{red}{-2} & = &20 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &20 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & 10x-x& = &20+2 \\\Leftrightarrow & 9x& = &22 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{22}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{22}{9} & & \\ & V = \left\{ \frac{22}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (2x+5)& = & -13 \color{red}{-} (-7+x) \\\Leftrightarrow & 8x+20& = &-13+7-x \\\Leftrightarrow & 8x \color{red}{+20} & = &-6 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 8x+x& = &-6-20 \\\Leftrightarrow & 9x& = &-26 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-26}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-26}{9} & & \\ & V = \left\{ \frac{-26}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-2x+1)& = & 1 \color{red}{+} (-5+x) \\\Leftrightarrow & -6x+3& = &1-5+x \\\Leftrightarrow & -6x \color{red}{+3} & = &-4 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & -6x-x& = &-4-3 \\\Leftrightarrow & -7x& = &-7 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-7}{ \color{red}{-7} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (4x-7)& = & 6 \color{red}{+} (-11+x) \\\Leftrightarrow & 24x-42& = &6-11+x \\\Leftrightarrow & 24x \color{red}{-42} & = &-5 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 24x-x& = &-5+42 \\\Leftrightarrow & 23x& = &37 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{37}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{37}{23} & & \\ & V = \left\{ \frac{37}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-x-7)& = & 15 \color{red}{+} (14-5x) \\\Leftrightarrow & -6x-42& = &15+14-5x \\\Leftrightarrow & -6x \color{red}{-42} & = &29 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-42} \color{blue}{+42} \color{blue}{+5x} & = &29 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+42} \\\Leftrightarrow & -6x+5x& = &29+42 \\\Leftrightarrow & -x& = &71 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{71}{ \color{red}{-1} } \\\Leftrightarrow & x = -71 & & \\ & V = \left\{ -71 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (x+1)& = & -9 \color{red}{-} (-5+x) \\\Leftrightarrow & 2x+2& = &-9+5-x \\\Leftrightarrow & 2x \color{red}{+2} & = &-4 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & 2x+x& = &-4-2 \\\Leftrightarrow & 3x& = &-6 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-6}{ \color{red}{3} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-4x+7)& = & -8 \color{red}{+} (-13+x) \\\Leftrightarrow & -12x+21& = &-8-13+x \\\Leftrightarrow & -12x \color{red}{+21} & = &-21 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+21} \color{blue}{-21} \color{blue}{-x} & = &-21 \color{red}{+x} \color{blue}{-x} \color{blue}{-21} \\\Leftrightarrow & -12x-x& = &-21-21 \\\Leftrightarrow & -13x& = &-42 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-42}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{42}{13} & & \\ & V = \left\{ \frac{42}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-4x+1)& = & -3 \color{red}{+} (-12+x) \\\Leftrightarrow & -12x+3& = &-3-12+x \\\Leftrightarrow & -12x \color{red}{+3} & = &-15 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & -12x-x& = &-15-3 \\\Leftrightarrow & -13x& = &-18 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-18}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{18}{13} & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)