Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (5x+3)& = & 15 \color{red}{-} (-15+3x) \\\Leftrightarrow & 25x+15& = &15+15-3x \\\Leftrightarrow & 25x \color{red}{+15} & = &30 \color{red}{-3x} \\\Leftrightarrow & 25x \color{red}{+15} \color{blue}{-15} \color{blue}{+3x} & = &30 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-15} \\\Leftrightarrow & 25x+3x& = &30-15 \\\Leftrightarrow & 28x& = &15 \\\Leftrightarrow & \frac{28x}{ \color{red}{28} }& = &\frac{15}{ \color{red}{28} } \\\Leftrightarrow & x = \frac{15}{28} & & \\ & V = \left\{ \frac{15}{28} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (2x+7)& = & -14 \color{red}{-} (-5+x) \\\Leftrightarrow & 12x+42& = &-14+5-x \\\Leftrightarrow & 12x \color{red}{+42} & = &-9 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & 12x+x& = &-9-42 \\\Leftrightarrow & 13x& = &-51 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-51}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-51}{13} & & \\ & V = \left\{ \frac{-51}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (4x+2)& = & 4 \color{red}{+} (3+3x) \\\Leftrightarrow & 8x+4& = &4+3+3x \\\Leftrightarrow & 8x \color{red}{+4} & = &7 \color{red}{+3x} \\\Leftrightarrow & 8x \color{red}{+4} \color{blue}{-4} \color{blue}{-3x} & = &7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-4} \\\Leftrightarrow & 8x-3x& = &7-4 \\\Leftrightarrow & 5x& = &3 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{3}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{3}{5} & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-3x+3)& = & -6 \color{red}{+} (-3+x) \\\Leftrightarrow & -6x+6& = &-6-3+x \\\Leftrightarrow & -6x \color{red}{+6} & = &-9 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -6x-x& = &-9-6 \\\Leftrightarrow & -7x& = &-15 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-15}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{15}{7} & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-x+2)& = & -6 \color{red}{-} (-14-3x) \\\Leftrightarrow & -4x+8& = &-6+14+3x \\\Leftrightarrow & -4x \color{red}{+8} & = &8 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+8} \color{blue}{-8} \color{blue}{-3x} & = &8 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-8} \\\Leftrightarrow & -4x-3x& = &8-8 \\\Leftrightarrow & -7x& = &0 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{0}{ \color{red}{-7} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (5x-4)& = & -9 \color{red}{+} (-7-2x) \\\Leftrightarrow & 15x-12& = &-9-7-2x \\\Leftrightarrow & 15x \color{red}{-12} & = &-16 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-12} \color{blue}{+12} \color{blue}{+2x} & = &-16 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+12} \\\Leftrightarrow & 15x+2x& = &-16+12 \\\Leftrightarrow & 17x& = &-4 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-4}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-4}{17} & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (4x+5)& = & -14 \color{red}{+} (9+x) \\\Leftrightarrow & 24x+30& = &-14+9+x \\\Leftrightarrow & 24x \color{red}{+30} & = &-5 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 24x-x& = &-5-30 \\\Leftrightarrow & 23x& = &-35 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-35}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-35}{23} & & \\ & V = \left\{ \frac{-35}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-5x-4)& = & -14 \color{red}{-} (7-3x) \\\Leftrightarrow & -10x-8& = &-14-7+3x \\\Leftrightarrow & -10x \color{red}{-8} & = &-21 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &-21 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & -10x-3x& = &-21+8 \\\Leftrightarrow & -13x& = &-13 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-13}{ \color{red}{-13} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-x-5)& = & -10 \color{red}{+} (-11-4x) \\\Leftrightarrow & -5x-25& = &-10-11-4x \\\Leftrightarrow & -5x \color{red}{-25} & = &-21 \color{red}{-4x} \\\Leftrightarrow & -5x \color{red}{-25} \color{blue}{+25} \color{blue}{+4x} & = &-21 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+25} \\\Leftrightarrow & -5x+4x& = &-21+25 \\\Leftrightarrow & -x& = &4 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{4}{ \color{red}{-1} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (5x-5)& = & 15 \color{red}{+} (-4-2x) \\\Leftrightarrow & 15x-15& = &15-4-2x \\\Leftrightarrow & 15x \color{red}{-15} & = &11 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-15} \color{blue}{+15} \color{blue}{+2x} & = &11 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+15} \\\Leftrightarrow & 15x+2x& = &11+15 \\\Leftrightarrow & 17x& = &26 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{26}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{26}{17} & & \\ & V = \left\{ \frac{26}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (6x+3)& = & 4 \color{red}{+} (4+x) \\\Leftrightarrow & 12x+6& = &4+4+x \\\Leftrightarrow & 12x \color{red}{+6} & = &8 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 12x-x& = &8-6 \\\Leftrightarrow & 11x& = &2 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{2}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (2x+4)& = & 11 \color{red}{-} (11+x) \\\Leftrightarrow & 6x+12& = &11-11-x \\\Leftrightarrow & 6x \color{red}{+12} & = &0 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 6x+x& = &0-12 \\\Leftrightarrow & 7x& = &-12 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-12}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-12}{7} & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)