Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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