Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (4x-3)& = & -5 \color{red}{+} (5+x) \\\Leftrightarrow & 12x-9& = &-5+5+x \\\Leftrightarrow & 12x \color{red}{-9} & = &0 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-9} \color{blue}{+9} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+9} \\\Leftrightarrow & 12x-x& = &0+9 \\\Leftrightarrow & 11x& = &9 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{9}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{9}{11} & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-4x+5)& = & -14 \color{red}{+} (8+x) \\\Leftrightarrow & -24x+30& = &-14+8+x \\\Leftrightarrow & -24x \color{red}{+30} & = &-6 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -24x-x& = &-6-30 \\\Leftrightarrow & -25x& = &-36 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-36}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{36}{25} & & \\ & V = \left\{ \frac{36}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (x+3)& = & -1 \color{red}{-} (8+x) \\\Leftrightarrow & 6x+18& = &-1-8-x \\\Leftrightarrow & 6x \color{red}{+18} & = &-9 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 6x+x& = &-9-18 \\\Leftrightarrow & 7x& = &-27 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-27}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-27}{7} & & \\ & V = \left\{ \frac{-27}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-5x-1)& = & -10 \color{red}{+} (15-4x) \\\Leftrightarrow & -25x-5& = &-10+15-4x \\\Leftrightarrow & -25x \color{red}{-5} & = &5 \color{red}{-4x} \\\Leftrightarrow & -25x \color{red}{-5} \color{blue}{+5} \color{blue}{+4x} & = &5 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+5} \\\Leftrightarrow & -25x+4x& = &5+5 \\\Leftrightarrow & -21x& = &10 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{10}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-10}{21} & & \\ & V = \left\{ \frac{-10}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-3x-2)& = & -3 \color{red}{+} (9+x) \\\Leftrightarrow & -12x-8& = &-3+9+x \\\Leftrightarrow & -12x \color{red}{-8} & = &6 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -12x-x& = &6+8 \\\Leftrightarrow & -13x& = &14 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{14}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-14}{13} & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-x-4)& = & -1 \color{red}{+} (3+x) \\\Leftrightarrow & -3x-12& = &-1+3+x \\\Leftrightarrow & -3x \color{red}{-12} & = &2 \color{red}{+x} \\\Leftrightarrow & -3x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -3x-x& = &2+12 \\\Leftrightarrow & -4x& = &14 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{14}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{-7}{2} & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (3x-6)& = & 7 \color{red}{-} (-15-5x) \\\Leftrightarrow & 18x-36& = &7+15+5x \\\Leftrightarrow & 18x \color{red}{-36} & = &22 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-36} \color{blue}{+36} \color{blue}{-5x} & = &22 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+36} \\\Leftrightarrow & 18x-5x& = &22+36 \\\Leftrightarrow & 13x& = &58 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{58}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{58}{13} & & \\ & V = \left\{ \frac{58}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (3x-4)& = & -11 \color{red}{+} (5+x) \\\Leftrightarrow & 9x-12& = &-11+5+x \\\Leftrightarrow & 9x \color{red}{-12} & = &-6 \color{red}{+x} \\\Leftrightarrow & 9x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 9x-x& = &-6+12 \\\Leftrightarrow & 8x& = &6 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{6}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{3}{4} & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-6x-7)& = & 4 \color{red}{+} (11-5x) \\\Leftrightarrow & -18x-21& = &4+11-5x \\\Leftrightarrow & -18x \color{red}{-21} & = &15 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-21} \color{blue}{+21} \color{blue}{+5x} & = &15 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+21} \\\Leftrightarrow & -18x+5x& = &15+21 \\\Leftrightarrow & -13x& = &36 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{36}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-36}{13} & & \\ & V = \left\{ \frac{-36}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (2x+3)& = & 14 \color{red}{+} (12-3x) \\\Leftrightarrow & 4x+6& = &14+12-3x \\\Leftrightarrow & 4x \color{red}{+6} & = &26 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+6} \color{blue}{-6} \color{blue}{+3x} & = &26 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-6} \\\Leftrightarrow & 4x+3x& = &26-6 \\\Leftrightarrow & 7x& = &20 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{20}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{20}{7} & & \\ & V = \left\{ \frac{20}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-5x+4)& = & 5 \color{red}{-} (-12+3x) \\\Leftrightarrow & -25x+20& = &5+12-3x \\\Leftrightarrow & -25x \color{red}{+20} & = &17 \color{red}{-3x} \\\Leftrightarrow & -25x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &17 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & -25x+3x& = &17-20 \\\Leftrightarrow & -22x& = &-3 \\\Leftrightarrow & \frac{-22x}{ \color{red}{-22} }& = &\frac{-3}{ \color{red}{-22} } \\\Leftrightarrow & x = \frac{3}{22} & & \\ & V = \left\{ \frac{3}{22} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-x+6)& = & 10 \color{red}{+} (-13-3x) \\\Leftrightarrow & -4x+24& = &10-13-3x \\\Leftrightarrow & -4x \color{red}{+24} & = &-3 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+24} \color{blue}{-24} \color{blue}{+3x} & = &-3 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-24} \\\Leftrightarrow & -4x+3x& = &-3-24 \\\Leftrightarrow & -x& = &-27 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-27}{ \color{red}{-1} } \\\Leftrightarrow & x = 27 & & \\ & V = \left\{ 27 \right\} & \\\end{align}\)