Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (4x+4)& = & -8 \color{red}{-} (-15+x) \\\Leftrightarrow & 20x+20& = &-8+15-x \\\Leftrightarrow & 20x \color{red}{+20} & = &7 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 20x+x& = &7-20 \\\Leftrightarrow & 21x& = &-13 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-13}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-13}{21} & & \\ & V = \left\{ \frac{-13}{21} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (3x-3)& = & 10 \color{red}{+} (13-5x) \\\Leftrightarrow & 6x-6& = &10+13-5x \\\Leftrightarrow & 6x \color{red}{-6} & = &23 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &23 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & 6x+5x& = &23+6 \\\Leftrightarrow & 11x& = &29 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{29}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{29}{11} & & \\ & V = \left\{ \frac{29}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (x+4)& = & 2 \color{red}{-} (11+x) \\\Leftrightarrow & 2x+8& = &2-11-x \\\Leftrightarrow & 2x \color{red}{+8} & = &-9 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 2x+x& = &-9-8 \\\Leftrightarrow & 3x& = &-17 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-17}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-17}{3} & & \\ & V = \left\{ \frac{-17}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-4x-5)& = & -8 \color{red}{+} (-6-5x) \\\Leftrightarrow & -16x-20& = &-8-6-5x \\\Leftrightarrow & -16x \color{red}{-20} & = &-14 \color{red}{-5x} \\\Leftrightarrow & -16x \color{red}{-20} \color{blue}{+20} \color{blue}{+5x} & = &-14 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+20} \\\Leftrightarrow & -16x+5x& = &-14+20 \\\Leftrightarrow & -11x& = &6 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{6}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-6}{11} & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-6x+1)& = & -4 \color{red}{-} (1+x) \\\Leftrightarrow & -30x+5& = &-4-1-x \\\Leftrightarrow & -30x \color{red}{+5} & = &-5 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & -30x+x& = &-5-5 \\\Leftrightarrow & -29x& = &-10 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-10}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{10}{29} & & \\ & V = \left\{ \frac{10}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-2x+3)& = & 1 \color{red}{-} (3+x) \\\Leftrightarrow & -8x+12& = &1-3-x \\\Leftrightarrow & -8x \color{red}{+12} & = &-2 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -8x+x& = &-2-12 \\\Leftrightarrow & -7x& = &-14 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-14}{ \color{red}{-7} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-2x+2)& = & -10 \color{red}{-} (-11-3x) \\\Leftrightarrow & -4x+4& = &-10+11+3x \\\Leftrightarrow & -4x \color{red}{+4} & = &1 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+4} \color{blue}{-4} \color{blue}{-3x} & = &1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-4} \\\Leftrightarrow & -4x-3x& = &1-4 \\\Leftrightarrow & -7x& = &-3 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-3}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (6x-4)& = & -1 \color{red}{-} (-4+x) \\\Leftrightarrow & 12x-8& = &-1+4-x \\\Leftrightarrow & 12x \color{red}{-8} & = &3 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 12x+x& = &3+8 \\\Leftrightarrow & 13x& = &11 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{11}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{11}{13} & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-3x+5)& = & 6 \color{red}{+} (-15+x) \\\Leftrightarrow & -15x+25& = &6-15+x \\\Leftrightarrow & -15x \color{red}{+25} & = &-9 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & -15x-x& = &-9-25 \\\Leftrightarrow & -16x& = &-34 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{-34}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{17}{8} & & \\ & V = \left\{ \frac{17}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (6x-4)& = & -1 \color{red}{+} (3-5x) \\\Leftrightarrow & 36x-24& = &-1+3-5x \\\Leftrightarrow & 36x \color{red}{-24} & = &2 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{-24} \color{blue}{+24} \color{blue}{+5x} & = &2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+24} \\\Leftrightarrow & 36x+5x& = &2+24 \\\Leftrightarrow & 41x& = &26 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{26}{ \color{red}{41} } \\\Leftrightarrow & x = \frac{26}{41} & & \\ & V = \left\{ \frac{26}{41} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-2x-4)& = & -6 \color{red}{+} (6+x) \\\Leftrightarrow & -4x-8& = &-6+6+x \\\Leftrightarrow & -4x \color{red}{-8} & = &0 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -4x-x& = &0+8 \\\Leftrightarrow & -5x& = &8 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{8}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-8}{5} & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-6x+1)& = & 5 \color{red}{-} (-10+x) \\\Leftrightarrow & -24x+4& = &5+10-x \\\Leftrightarrow & -24x \color{red}{+4} & = &15 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -24x+x& = &15-4 \\\Leftrightarrow & -23x& = &11 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{11}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-11}{23} & & \\ & V = \left\{ \frac{-11}{23} \right\} & \\\end{align}\)