Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-6x-2)& = & 4 \color{red}{-} (-3+x) \\\Leftrightarrow & -24x-8& = &4+3-x \\\Leftrightarrow & -24x \color{red}{-8} & = &7 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -24x+x& = &7+8 \\\Leftrightarrow & -23x& = &15 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{15}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-15}{23} & & \\ & V = \left\{ \frac{-15}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-2x-1)& = & -6 \color{red}{-} (-1+x) \\\Leftrightarrow & -12x-6& = &-6+1-x \\\Leftrightarrow & -12x \color{red}{-6} & = &-5 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -12x+x& = &-5+6 \\\Leftrightarrow & -11x& = &1 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{1}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-1}{11} & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-x+2)& = & -6 \color{red}{-} (2+3x) \\\Leftrightarrow & -4x+8& = &-6-2-3x \\\Leftrightarrow & -4x \color{red}{+8} & = &-8 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+8} \color{blue}{-8} \color{blue}{+3x} & = &-8 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-8} \\\Leftrightarrow & -4x+3x& = &-8-8 \\\Leftrightarrow & -x& = &-16 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-16}{ \color{red}{-1} } \\\Leftrightarrow & x = 16 & & \\ & V = \left\{ 16 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-x-4)& = & -2 \color{red}{-} (-13+3x) \\\Leftrightarrow & -4x-16& = &-2+13-3x \\\Leftrightarrow & -4x \color{red}{-16} & = &11 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-16} \color{blue}{+16} \color{blue}{+3x} & = &11 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+16} \\\Leftrightarrow & -4x+3x& = &11+16 \\\Leftrightarrow & -x& = &27 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{27}{ \color{red}{-1} } \\\Leftrightarrow & x = -27 & & \\ & V = \left\{ -27 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (6x-5)& = & -1 \color{red}{-} (13+x) \\\Leftrightarrow & 24x-20& = &-1-13-x \\\Leftrightarrow & 24x \color{red}{-20} & = &-14 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 24x+x& = &-14+20 \\\Leftrightarrow & 25x& = &6 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{6}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{6}{25} & & \\ & V = \left\{ \frac{6}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-2x-5)& = & 9 \color{red}{+} (5+x) \\\Leftrightarrow & -10x-25& = &9+5+x \\\Leftrightarrow & -10x \color{red}{-25} & = &14 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-25} \color{blue}{+25} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{+25} \\\Leftrightarrow & -10x-x& = &14+25 \\\Leftrightarrow & -11x& = &39 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{39}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-39}{11} & & \\ & V = \left\{ \frac{-39}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-3x-2)& = & -14 \color{red}{-} (-3+x) \\\Leftrightarrow & -6x-4& = &-14+3-x \\\Leftrightarrow & -6x \color{red}{-4} & = &-11 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -6x+x& = &-11+4 \\\Leftrightarrow & -5x& = &-7 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-7}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{7}{5} & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (4x-4)& = & -9 \color{red}{+} (-14+x) \\\Leftrightarrow & 8x-8& = &-9-14+x \\\Leftrightarrow & 8x \color{red}{-8} & = &-23 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-23 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 8x-x& = &-23+8 \\\Leftrightarrow & 7x& = &-15 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-15}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-15}{7} & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (x-7)& = & -14 \color{red}{-} (6+x) \\\Leftrightarrow & 2x-14& = &-14-6-x \\\Leftrightarrow & 2x \color{red}{-14} & = &-20 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & 2x+x& = &-20+14 \\\Leftrightarrow & 3x& = &-6 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-6}{ \color{red}{3} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-6x-6)& = & -3 \color{red}{+} (-14+x) \\\Leftrightarrow & -24x-24& = &-3-14+x \\\Leftrightarrow & -24x \color{red}{-24} & = &-17 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -24x-x& = &-17+24 \\\Leftrightarrow & -25x& = &7 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{7}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-7}{25} & & \\ & V = \left\{ \frac{-7}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (4x+1)& = & 4 \color{red}{-} (10+x) \\\Leftrightarrow & 20x+5& = &4-10-x \\\Leftrightarrow & 20x \color{red}{+5} & = &-6 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & 20x+x& = &-6-5 \\\Leftrightarrow & 21x& = &-11 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-11}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-11}{21} & & \\ & V = \left\{ \frac{-11}{21} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-5x-6)& = & 7 \color{red}{-} (6+x) \\\Leftrightarrow & -30x-36& = &7-6-x \\\Leftrightarrow & -30x \color{red}{-36} & = &1 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & -30x+x& = &1+36 \\\Leftrightarrow & -29x& = &37 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{37}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-37}{29} & & \\ & V = \left\{ \frac{-37}{29} \right\} & \\\end{align}\)