Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{+11}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+11}\color{blue}{-11-x } & = & -2 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -2 \color{blue}{-11} \\\Leftrightarrow &-13x & = &-13\\\Leftrightarrow & \color{red}{-13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-13}{-13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{+7}& = & -5 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{+7}\color{blue}{-7+10x } & = & -5 \color{red}{ -10x }\color{blue}{-7+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & -5 \color{blue}{-7} \\\Leftrightarrow &21x & = &-12\\\Leftrightarrow & \color{red}{21}x & = &-12\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-12}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{+4}& = & 7 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+4}\color{blue}{-4+3x } & = & 7 \color{red}{ -3x }\color{blue}{-4+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & 7 \color{blue}{-4} \\\Leftrightarrow &10x & = &3\\\Leftrightarrow & \color{red}{10}x & = &3\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{3}{10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{10} } & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{+15}& = & 7 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15+6x } & = & 7 \color{red}{ -6x }\color{blue}{-15+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 7 \color{blue}{-15} \\\Leftrightarrow &19x & = &-8\\\Leftrightarrow & \color{red}{19}x & = &-8\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-8}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{19} } & & \\ & V = \left\{ \frac{-8}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+4}& = & 9 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{+4}\color{blue}{-4-11x } & = & 9 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & 9 \color{blue}{-4} \\\Leftrightarrow &x & = &5\\\Leftrightarrow & \color{red}{}x & = &5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 5 \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{+9}& = & 6 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{+9}\color{blue}{-9-4x } & = & 6 \color{red}{ +4x }\color{blue}{-9-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & 6 \color{blue}{-9} \\\Leftrightarrow &-11x & = &-3\\\Leftrightarrow & \color{red}{-11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{-2}& = & -11 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-2}\color{blue}{+2+6x } & = & -11 \color{red}{ -6x }\color{blue}{+2+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -11 \color{blue}{+2} \\\Leftrightarrow &19x & = &-9\\\Leftrightarrow & \color{red}{19}x & = &-9\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-9}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{19} } & & \\ & V = \left\{ \frac{-9}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{-10}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10-x } & = & -7 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -7 \color{blue}{+10} \\\Leftrightarrow &-11x & = &3\\\Leftrightarrow & \color{red}{-11}x & = &3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{-9}& = & -9 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-9}\color{blue}{+9+3x } & = & -9 \color{red}{ -3x }\color{blue}{+9+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -9 \color{blue}{+9} \\\Leftrightarrow &13x & = &0\\\Leftrightarrow & \color{red}{13}x & = &0\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{0}{13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{-5}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-5}\color{blue}{+5-x } & = & 3 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 3 \color{blue}{+5} \\\Leftrightarrow &-14x & = &8\\\Leftrightarrow & \color{red}{-14}x & = &8\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{8}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{-14}& = & 3 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-14}\color{blue}{+14-7x } & = & 3 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 3 \color{blue}{+14} \\\Leftrightarrow &3x & = &17\\\Leftrightarrow & \color{red}{3}x & = &17\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{17}{3} \\\Leftrightarrow & \color{green}{ x = \frac{17}{3} } & & \\ & V = \left\{ \frac{17}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{+5}& = & 9 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{+5}\color{blue}{-5-4x } & = & 9 \color{red}{ +4x }\color{blue}{-5-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & 9 \color{blue}{-5} \\\Leftrightarrow &5x & = &4\\\Leftrightarrow & \color{red}{5}x & = &4\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{4}{5} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)