Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (4x+7)& = & -8 \color{red}{+} (5-5x) \\\Leftrightarrow & 16x+28& = &-8+5-5x \\\Leftrightarrow & 16x \color{red}{+28} & = &-3 \color{red}{-5x} \\\Leftrightarrow & 16x \color{red}{+28} \color{blue}{-28} \color{blue}{+5x} & = &-3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-28} \\\Leftrightarrow & 16x+5x& = &-3-28 \\\Leftrightarrow & 21x& = &-31 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-31}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-31}{21} & & \\ & V = \left\{ \frac{-31}{21} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-5x+7)& = & 12 \color{red}{+} (-14-4x) \\\Leftrightarrow & -25x+35& = &12-14-4x \\\Leftrightarrow & -25x \color{red}{+35} & = &-2 \color{red}{-4x} \\\Leftrightarrow & -25x \color{red}{+35} \color{blue}{-35} \color{blue}{+4x} & = &-2 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-35} \\\Leftrightarrow & -25x+4x& = &-2-35 \\\Leftrightarrow & -21x& = &-37 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-37}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{37}{21} & & \\ & V = \left\{ \frac{37}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (3x+4)& = & 3 \color{red}{+} (7-2x) \\\Leftrightarrow & 15x+20& = &3+7-2x \\\Leftrightarrow & 15x \color{red}{+20} & = &10 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+20} \color{blue}{-20} \color{blue}{+2x} & = &10 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-20} \\\Leftrightarrow & 15x+2x& = &10-20 \\\Leftrightarrow & 17x& = &-10 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-10}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-10}{17} & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (3x-1)& = & 15 \color{red}{-} (-9+x) \\\Leftrightarrow & 12x-4& = &15+9-x \\\Leftrightarrow & 12x \color{red}{-4} & = &24 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &24 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 12x+x& = &24+4 \\\Leftrightarrow & 13x& = &28 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{28}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{28}{13} & & \\ & V = \left\{ \frac{28}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-6x+3)& = & 3 \color{red}{-} (-1+x) \\\Leftrightarrow & -24x+12& = &3+1-x \\\Leftrightarrow & -24x \color{red}{+12} & = &4 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -24x+x& = &4-12 \\\Leftrightarrow & -23x& = &-8 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-8}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{8}{23} & & \\ & V = \left\{ \frac{8}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (2x-1)& = & -9 \color{red}{+} (2-5x) \\\Leftrightarrow & 8x-4& = &-9+2-5x \\\Leftrightarrow & 8x \color{red}{-4} & = &-7 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{-4} \color{blue}{+4} \color{blue}{+5x} & = &-7 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+4} \\\Leftrightarrow & 8x+5x& = &-7+4 \\\Leftrightarrow & 13x& = &-3 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-3}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-3}{13} & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-3x-2)& = & 3 \color{red}{+} (-10+4x) \\\Leftrightarrow & -15x-10& = &3-10+4x \\\Leftrightarrow & -15x \color{red}{-10} & = &-7 \color{red}{+4x} \\\Leftrightarrow & -15x \color{red}{-10} \color{blue}{+10} \color{blue}{-4x} & = &-7 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+10} \\\Leftrightarrow & -15x-4x& = &-7+10 \\\Leftrightarrow & -19x& = &3 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{3}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-3}{19} & & \\ & V = \left\{ \frac{-3}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (3x+6)& = & 3 \color{red}{-} (-6-5x) \\\Leftrightarrow & 6x+12& = &3+6+5x \\\Leftrightarrow & 6x \color{red}{+12} & = &9 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &9 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & 6x-5x& = &9-12 \\\Leftrightarrow & x& = &-3 \\ & V = \left\{ -3 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-4x+4)& = & 11 \color{red}{+} (-15+x) \\\Leftrightarrow & -12x+12& = &11-15+x \\\Leftrightarrow & -12x \color{red}{+12} & = &-4 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -12x-x& = &-4-12 \\\Leftrightarrow & -13x& = &-16 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-16}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{16}{13} & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-6x+4)& = & -5 \color{red}{+} (-5+x) \\\Leftrightarrow & -36x+24& = &-5-5+x \\\Leftrightarrow & -36x \color{red}{+24} & = &-10 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -36x-x& = &-10-24 \\\Leftrightarrow & -37x& = &-34 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{-34}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{34}{37} & & \\ & V = \left\{ \frac{34}{37} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-5x-3)& = & 14 \color{red}{+} (-14+x) \\\Leftrightarrow & -20x-12& = &14-14+x \\\Leftrightarrow & -20x \color{red}{-12} & = &0 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -20x-x& = &0+12 \\\Leftrightarrow & -21x& = &12 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{12}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-4}{7} & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (4x-3)& = & 5 \color{red}{+} (-8+x) \\\Leftrightarrow & 8x-6& = &5-8+x \\\Leftrightarrow & 8x \color{red}{-6} & = &-3 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 8x-x& = &-3+6 \\\Leftrightarrow & 7x& = &3 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{3}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)