Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-2x-7)& = & -13 \color{red}{-} (13+x) \\\Leftrightarrow & -10x-35& = &-13-13-x \\\Leftrightarrow & -10x \color{red}{-35} & = &-26 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &-26 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & -10x+x& = &-26+35 \\\Leftrightarrow & -9x& = &9 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{9}{ \color{red}{-9} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-2x-2)& = & -10 \color{red}{-} (1+3x) \\\Leftrightarrow & -4x-4& = &-10-1-3x \\\Leftrightarrow & -4x \color{red}{-4} & = &-11 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &-11 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & -4x+3x& = &-11+4 \\\Leftrightarrow & -x& = &-7 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-7}{ \color{red}{-1} } \\\Leftrightarrow & x = 7 & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-6x+2)& = & 8 \color{red}{+} (-12+x) \\\Leftrightarrow & -12x+4& = &8-12+x \\\Leftrightarrow & -12x \color{red}{+4} & = &-4 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & -12x-x& = &-4-4 \\\Leftrightarrow & -13x& = &-8 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-8}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (4x+2)& = & 13 \color{red}{+} (15+3x) \\\Leftrightarrow & 8x+4& = &13+15+3x \\\Leftrightarrow & 8x \color{red}{+4} & = &28 \color{red}{+3x} \\\Leftrightarrow & 8x \color{red}{+4} \color{blue}{-4} \color{blue}{-3x} & = &28 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-4} \\\Leftrightarrow & 8x-3x& = &28-4 \\\Leftrightarrow & 5x& = &24 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{24}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{24}{5} & & \\ & V = \left\{ \frac{24}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-x+6)& = & -11 \color{red}{+} (-9-3x) \\\Leftrightarrow & -4x+24& = &-11-9-3x \\\Leftrightarrow & -4x \color{red}{+24} & = &-20 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+24} \color{blue}{-24} \color{blue}{+3x} & = &-20 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-24} \\\Leftrightarrow & -4x+3x& = &-20-24 \\\Leftrightarrow & -x& = &-44 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-44}{ \color{red}{-1} } \\\Leftrightarrow & x = 44 & & \\ & V = \left\{ 44 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (6x+4)& = & -2 \color{red}{-} (-2-5x) \\\Leftrightarrow & 18x+12& = &-2+2+5x \\\Leftrightarrow & 18x \color{red}{+12} & = &0 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &0 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & 18x-5x& = &0-12 \\\Leftrightarrow & 13x& = &-12 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-12}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-12}{13} & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-6x-3)& = & -10 \color{red}{-} (-7-5x) \\\Leftrightarrow & -36x-18& = &-10+7+5x \\\Leftrightarrow & -36x \color{red}{-18} & = &-3 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{-18} \color{blue}{+18} \color{blue}{-5x} & = &-3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+18} \\\Leftrightarrow & -36x-5x& = &-3+18 \\\Leftrightarrow & -41x& = &15 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{15}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{-15}{41} & & \\ & V = \left\{ \frac{-15}{41} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-5x+4)& = & 3 \color{red}{-} (13+x) \\\Leftrightarrow & -15x+12& = &3-13-x \\\Leftrightarrow & -15x \color{red}{+12} & = &-10 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -15x+x& = &-10-12 \\\Leftrightarrow & -14x& = &-22 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{-22}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{11}{7} & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (2x+3)& = & 11 \color{red}{+} (-7+3x) \\\Leftrightarrow & 10x+15& = &11-7+3x \\\Leftrightarrow & 10x \color{red}{+15} & = &4 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+15} \color{blue}{-15} \color{blue}{-3x} & = &4 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-15} \\\Leftrightarrow & 10x-3x& = &4-15 \\\Leftrightarrow & 7x& = &-11 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-11}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-11}{7} & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (5x+2)& = & -14 \color{red}{+} (4+4x) \\\Leftrightarrow & 15x+6& = &-14+4+4x \\\Leftrightarrow & 15x \color{red}{+6} & = &-10 \color{red}{+4x} \\\Leftrightarrow & 15x \color{red}{+6} \color{blue}{-6} \color{blue}{-4x} & = &-10 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-6} \\\Leftrightarrow & 15x-4x& = &-10-6 \\\Leftrightarrow & 11x& = &-16 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-16}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-16}{11} & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-2x+2)& = & 5 \color{red}{+} (6+x) \\\Leftrightarrow & -12x+12& = &5+6+x \\\Leftrightarrow & -12x \color{red}{+12} & = &11 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -12x-x& = &11-12 \\\Leftrightarrow & -13x& = &-1 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-1}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-4x-7)& = & 13 \color{red}{-} (-8+x) \\\Leftrightarrow & -12x-21& = &13+8-x \\\Leftrightarrow & -12x \color{red}{-21} & = &21 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-21} \color{blue}{+21} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{+21} \\\Leftrightarrow & -12x+x& = &21+21 \\\Leftrightarrow & -11x& = &42 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{42}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-42}{11} & & \\ & V = \left\{ \frac{-42}{11} \right\} & \\\end{align}\)