Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (2x-6)& = & 13 \color{red}{+} (9+x) \\\Leftrightarrow & 8x-24& = &13+9+x \\\Leftrightarrow & 8x \color{red}{-24} & = &22 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &22 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 8x-x& = &22+24 \\\Leftrightarrow & 7x& = &46 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{46}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{46}{7} & & \\ & V = \left\{ \frac{46}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (4x-5)& = & 9 \color{red}{+} (6+x) \\\Leftrightarrow & 16x-20& = &9+6+x \\\Leftrightarrow & 16x \color{red}{-20} & = &15 \color{red}{+x} \\\Leftrightarrow & 16x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 16x-x& = &15+20 \\\Leftrightarrow & 15x& = &35 \\\Leftrightarrow & \frac{15x}{ \color{red}{15} }& = &\frac{35}{ \color{red}{15} } \\\Leftrightarrow & x = \frac{7}{3} & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (x+3)& = & 6 \color{red}{-} (4+x) \\\Leftrightarrow & 6x+18& = &6-4-x \\\Leftrightarrow & 6x \color{red}{+18} & = &2 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 6x+x& = &2-18 \\\Leftrightarrow & 7x& = &-16 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-16}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-16}{7} & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-2x+7)& = & -10 \color{red}{-} (10+x) \\\Leftrightarrow & -4x+14& = &-10-10-x \\\Leftrightarrow & -4x \color{red}{+14} & = &-20 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & -4x+x& = &-20-14 \\\Leftrightarrow & -3x& = &-34 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-34}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{34}{3} & & \\ & V = \left\{ \frac{34}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-2x-3)& = & -15 \color{red}{-} (-14+x) \\\Leftrightarrow & -4x-6& = &-15+14-x \\\Leftrightarrow & -4x \color{red}{-6} & = &-1 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -4x+x& = &-1+6 \\\Leftrightarrow & -3x& = &5 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{5}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-5}{3} & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-5x-3)& = & 4 \color{red}{-} (-3+x) \\\Leftrightarrow & -20x-12& = &4+3-x \\\Leftrightarrow & -20x \color{red}{-12} & = &7 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -20x+x& = &7+12 \\\Leftrightarrow & -19x& = &19 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{19}{ \color{red}{-19} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-2x+4)& = & 4 \color{red}{+} (4+x) \\\Leftrightarrow & -4x+8& = &4+4+x \\\Leftrightarrow & -4x \color{red}{+8} & = &8 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -4x-x& = &8-8 \\\Leftrightarrow & -5x& = &0 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{0}{ \color{red}{-5} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (6x+6)& = & 14 \color{red}{-} (5+x) \\\Leftrightarrow & 12x+12& = &14-5-x \\\Leftrightarrow & 12x \color{red}{+12} & = &9 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 12x+x& = &9-12 \\\Leftrightarrow & 13x& = &-3 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-3}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-3}{13} & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-6x-5)& = & -11 \color{red}{-} (6+x) \\\Leftrightarrow & -24x-20& = &-11-6-x \\\Leftrightarrow & -24x \color{red}{-20} & = &-17 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & -24x+x& = &-17+20 \\\Leftrightarrow & -23x& = &3 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{3}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-3}{23} & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (6x+2)& = & 13 \color{red}{-} (-1+x) \\\Leftrightarrow & 18x+6& = &13+1-x \\\Leftrightarrow & 18x \color{red}{+6} & = &14 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 18x+x& = &14-6 \\\Leftrightarrow & 19x& = &8 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{8}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{8}{19} & & \\ & V = \left\{ \frac{8}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (2x-5)& = & -2 \color{red}{+} (-9+3x) \\\Leftrightarrow & 4x-10& = &-2-9+3x \\\Leftrightarrow & 4x \color{red}{-10} & = &-11 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &-11 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & 4x-3x& = &-11+10 \\\Leftrightarrow & x& = &-1 \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-5x+6)& = & -8 \color{red}{+} (-7-2x) \\\Leftrightarrow & -15x+18& = &-8-7-2x \\\Leftrightarrow & -15x \color{red}{+18} & = &-15 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+18} \color{blue}{-18} \color{blue}{+2x} & = &-15 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-18} \\\Leftrightarrow & -15x+2x& = &-15-18 \\\Leftrightarrow & -13x& = &-33 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-33}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{33}{13} & & \\ & V = \left\{ \frac{33}{13} \right\} & \\\end{align}\)