Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (x-5)& = & 11 \color{red}{-} (7+3x) \\\Leftrightarrow & 5x-25& = &11-7-3x \\\Leftrightarrow & 5x \color{red}{-25} & = &4 \color{red}{-3x} \\\Leftrightarrow & 5x \color{red}{-25} \color{blue}{+25} \color{blue}{+3x} & = &4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+25} \\\Leftrightarrow & 5x+3x& = &4+25 \\\Leftrightarrow & 8x& = &29 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{29}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{29}{8} & & \\ & V = \left\{ \frac{29}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (3x+4)& = & -6 \color{red}{-} (-12+x) \\\Leftrightarrow & 6x+8& = &-6+12-x \\\Leftrightarrow & 6x \color{red}{+8} & = &6 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 6x+x& = &6-8 \\\Leftrightarrow & 7x& = &-2 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-2}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-5x+5)& = & 3 \color{red}{-} (-10+x) \\\Leftrightarrow & -20x+20& = &3+10-x \\\Leftrightarrow & -20x \color{red}{+20} & = &13 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -20x+x& = &13-20 \\\Leftrightarrow & -19x& = &-7 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-7}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{7}{19} & & \\ & V = \left\{ \frac{7}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (6x+3)& = & -11 \color{red}{-} (11+x) \\\Leftrightarrow & 30x+15& = &-11-11-x \\\Leftrightarrow & 30x \color{red}{+15} & = &-22 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 30x+x& = &-22-15 \\\Leftrightarrow & 31x& = &-37 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-37}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-37}{31} & & \\ & V = \left\{ \frac{-37}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (3x-4)& = & 4 \color{red}{+} (5-2x) \\\Leftrightarrow & 15x-20& = &4+5-2x \\\Leftrightarrow & 15x \color{red}{-20} & = &9 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-20} \color{blue}{+20} \color{blue}{+2x} & = &9 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+20} \\\Leftrightarrow & 15x+2x& = &9+20 \\\Leftrightarrow & 17x& = &29 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{29}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{29}{17} & & \\ & V = \left\{ \frac{29}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (3x-5)& = & -13 \color{red}{-} (-13+x) \\\Leftrightarrow & 12x-20& = &-13+13-x \\\Leftrightarrow & 12x \color{red}{-20} & = &0 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 12x+x& = &0+20 \\\Leftrightarrow & 13x& = &20 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{20}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{20}{13} & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (4x+4)& = & -7 \color{red}{-} (10+x) \\\Leftrightarrow & 20x+20& = &-7-10-x \\\Leftrightarrow & 20x \color{red}{+20} & = &-17 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 20x+x& = &-17-20 \\\Leftrightarrow & 21x& = &-37 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-37}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-37}{21} & & \\ & V = \left\{ \frac{-37}{21} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (4x-4)& = & -7 \color{red}{-} (-15+x) \\\Leftrightarrow & 12x-12& = &-7+15-x \\\Leftrightarrow & 12x \color{red}{-12} & = &8 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 12x+x& = &8+12 \\\Leftrightarrow & 13x& = &20 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{20}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{20}{13} & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (6x-5)& = & 7 \color{red}{-} (-13+x) \\\Leftrightarrow & 30x-25& = &7+13-x \\\Leftrightarrow & 30x \color{red}{-25} & = &20 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & 30x+x& = &20+25 \\\Leftrightarrow & 31x& = &45 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{45}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{45}{31} & & \\ & V = \left\{ \frac{45}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-3x-5)& = & -4 \color{red}{-} (-8+x) \\\Leftrightarrow & -12x-20& = &-4+8-x \\\Leftrightarrow & -12x \color{red}{-20} & = &4 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & -12x+x& = &4+20 \\\Leftrightarrow & -11x& = &24 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{24}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-24}{11} & & \\ & V = \left\{ \frac{-24}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (4x+5)& = & -2 \color{red}{-} (-14+x) \\\Leftrightarrow & 12x+15& = &-2+14-x \\\Leftrightarrow & 12x \color{red}{+15} & = &12 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 12x+x& = &12-15 \\\Leftrightarrow & 13x& = &-3 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-3}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-3}{13} & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-6x+4)& = & 15 \color{red}{-} (2+x) \\\Leftrightarrow & -30x+20& = &15-2-x \\\Leftrightarrow & -30x \color{red}{+20} & = &13 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -30x+x& = &13-20 \\\Leftrightarrow & -29x& = &-7 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-7}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{7}{29} & & \\ & V = \left\{ \frac{7}{29} \right\} & \\\end{align}\)