Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{-15}& = & -10 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15+2x } & = & -10 \color{red}{ -2x }\color{blue}{+15+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & -10 \color{blue}{+15} \\\Leftrightarrow &13x & = &5\\\Leftrightarrow & \color{red}{13}x & = &5\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{5}{13} \\\Leftrightarrow & \color{green}{ x = \frac{5}{13} } & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+15}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+15}\color{blue}{-15-x } & = & -14 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -14 \color{blue}{-15} \\\Leftrightarrow &-3x & = &-29\\\Leftrightarrow & \color{red}{-3}x & = &-29\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-29}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{29}{3} } & & \\ & V = \left\{ \frac{29}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{-7}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-7}\color{blue}{+7-x } & = & 5 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 5 \color{blue}{+7} \\\Leftrightarrow &-7x & = &12\\\Leftrightarrow & \color{red}{-7}x & = &12\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{12}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{-9}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-9}\color{blue}{+9-x } & = & -2 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -2 \color{blue}{+9} \\\Leftrightarrow &-15x & = &7\\\Leftrightarrow & \color{red}{-15}x & = &7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{15} } & & \\ & V = \left\{ \frac{-7}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{+13}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+13}\color{blue}{-13-x } & = & 6 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 6 \color{blue}{-13} \\\Leftrightarrow &-12x & = &-7\\\Leftrightarrow & \color{red}{-12}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-7}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{-14}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-14}\color{blue}{+14-x } & = & -10 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -10 \color{blue}{+14} \\\Leftrightarrow &3x & = &4\\\Leftrightarrow & \color{red}{3}x & = &4\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{4}{3} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{+6}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+6}\color{blue}{-6-x } & = & -1 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -1 \color{blue}{-6} \\\Leftrightarrow &-12x & = &-7\\\Leftrightarrow & \color{red}{-12}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-7}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{+6}& = & 15 \color{red}{ +11x } \\\Leftrightarrow & 4x \color{red}{+6}\color{blue}{-6-11x } & = & 15 \color{red}{ +11x }\color{blue}{-6-11x } \\\Leftrightarrow & 4x \color{blue}{-11x } & = & 15 \color{blue}{-6} \\\Leftrightarrow &-7x & = &9\\\Leftrightarrow & \color{red}{-7}x & = &9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{-13}& = & -7 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{-13}\color{blue}{+13+2x } & = & -7 \color{red}{ -2x }\color{blue}{+13+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & -7 \color{blue}{+13} \\\Leftrightarrow &13x & = &6\\\Leftrightarrow & \color{red}{13}x & = &6\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{6}{13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{+11}& = & 11 \color{red}{ +9x } \\\Leftrightarrow & -2x \color{red}{+11}\color{blue}{-11-9x } & = & 11 \color{red}{ +9x }\color{blue}{-11-9x } \\\Leftrightarrow & -2x \color{blue}{-9x } & = & 11 \color{blue}{-11} \\\Leftrightarrow &-11x & = &0\\\Leftrightarrow & \color{red}{-11}x & = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{+5}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+5}\color{blue}{-5-x } & = & 13 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 13 \color{blue}{-5} \\\Leftrightarrow &-12x & = &8\\\Leftrightarrow & \color{red}{-12}x & = &8\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{8}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{+1}& = & 4 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{+1}\color{blue}{-1+11x } & = & 4 \color{red}{ -11x }\color{blue}{-1+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & 4 \color{blue}{-1} \\\Leftrightarrow &20x & = &3\\\Leftrightarrow & \color{red}{20}x & = &3\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{3}{20} \\\Leftrightarrow & \color{green}{ x = \frac{3}{20} } & & \\ & V = \left\{ \frac{3}{20} \right\} & \\\end{align}\)