Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{+11}& = & 4 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+11}\color{blue}{-11-14x } & = & 4 \color{red}{ +14x }\color{blue}{-11-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & 4 \color{blue}{-11} \\\Leftrightarrow &-23x & = &-7\\\Leftrightarrow & \color{red}{-23}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-7}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{7}{23} } & & \\ & V = \left\{ \frac{7}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{-1}& = & -15 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{-1}\color{blue}{+1+9x } & = & -15 \color{red}{ -9x }\color{blue}{+1+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & -15 \color{blue}{+1} \\\Leftrightarrow &23x & = &-14\\\Leftrightarrow & \color{red}{23}x & = &-14\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-14}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{23} } & & \\ & V = \left\{ \frac{-14}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{+11}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+11}\color{blue}{-11-13x } & = & -10 \color{red}{ +13x }\color{blue}{-11-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -10 \color{blue}{-11} \\\Leftrightarrow &-19x & = &-21\\\Leftrightarrow & \color{red}{-19}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-21}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{21}{19} } & & \\ & V = \left\{ \frac{21}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{+2}& = & 12 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+2}\color{blue}{-2+2x } & = & 12 \color{red}{ -2x }\color{blue}{-2+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 12 \color{blue}{-2} \\\Leftrightarrow &17x & = &10\\\Leftrightarrow & \color{red}{17}x & = &10\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{10}{17} \\\Leftrightarrow & \color{green}{ x = \frac{10}{17} } & & \\ & V = \left\{ \frac{10}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-13}& = & -5 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-13}\color{blue}{+13-11x } & = & -5 \color{red}{ +11x }\color{blue}{+13-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & -5 \color{blue}{+13} \\\Leftrightarrow &x & = &8\\\Leftrightarrow & \color{red}{}x & = &8\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 8 \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{+14}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+14}\color{blue}{-14-x } & = & -15 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -15 \color{blue}{-14} \\\Leftrightarrow &-7x & = &-29\\\Leftrightarrow & \color{red}{-7}x & = &-29\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-29}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{29}{7} } & & \\ & V = \left\{ \frac{29}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{-8}& = & -7 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-8}\color{blue}{+8-14x } & = & -7 \color{red}{ +14x }\color{blue}{+8-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -7 \color{blue}{+8} \\\Leftrightarrow &-27x & = &1\\\Leftrightarrow & \color{red}{-27}x & = &1\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{1}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{27} } & & \\ & V = \left\{ \frac{-1}{27} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{-11}& = & -9 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-11}\color{blue}{+11-11x } & = & -9 \color{red}{ +11x }\color{blue}{+11-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & -9 \color{blue}{+11} \\\Leftrightarrow &-21x & = &2\\\Leftrightarrow & \color{red}{-21}x & = &2\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{2}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{21} } & & \\ & V = \left\{ \frac{-2}{21} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{+5}& = & -9 \color{red}{ +11x } \\\Leftrightarrow & -8x \color{red}{+5}\color{blue}{-5-11x } & = & -9 \color{red}{ +11x }\color{blue}{-5-11x } \\\Leftrightarrow & -8x \color{blue}{-11x } & = & -9 \color{blue}{-5} \\\Leftrightarrow &-19x & = &-14\\\Leftrightarrow & \color{red}{-19}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-14}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{14}{19} } & & \\ & V = \left\{ \frac{14}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{-11}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-11}\color{blue}{+11-x } & = & 10 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 10 \color{blue}{+11} \\\Leftrightarrow &-15x & = &21\\\Leftrightarrow & \color{red}{-15}x & = &21\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{21}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{+4}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-x } & = & 6 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 6 \color{blue}{-4} \\\Leftrightarrow &-14x & = &2\\\Leftrightarrow & \color{red}{-14}x & = &2\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{2}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{+6}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{+6}\color{blue}{-6-5x } & = & -8 \color{red}{ +5x }\color{blue}{-6-5x } \\\Leftrightarrow & 2x \color{blue}{-5x } & = & -8 \color{blue}{-6} \\\Leftrightarrow &-3x & = &-14\\\Leftrightarrow & \color{red}{-3}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-14}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{14}{3} } & & \\ & V = \left\{ \frac{14}{3} \right\} & \\\end{align}\)