Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{+13}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+13}\color{blue}{-13-x } & = & 1 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 1 \color{blue}{-13} \\\Leftrightarrow &9x & = &-12\\\Leftrightarrow & \color{red}{9}x & = &-12\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-12}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{-6}& = & 15 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{-6}\color{blue}{+6+13x } & = & 15 \color{red}{ -13x }\color{blue}{+6+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & 15 \color{blue}{+6} \\\Leftrightarrow &21x & = &21\\\Leftrightarrow & \color{red}{21}x & = &21\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{21}{21} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{-1}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-1}\color{blue}{+1-x } & = & 13 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 13 \color{blue}{+1} \\\Leftrightarrow &-11x & = &14\\\Leftrightarrow & \color{red}{-11}x & = &14\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{14}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{11} } & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{+8}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+8}\color{blue}{-8-x } & = & 12 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 12 \color{blue}{-8} \\\Leftrightarrow &9x & = &4\\\Leftrightarrow & \color{red}{9}x & = &4\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{4}{9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+6}& = & -3 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+6}\color{blue}{-6+11x } & = & -3 \color{red}{ -11x }\color{blue}{-6+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -3 \color{blue}{-6} \\\Leftrightarrow &23x & = &-9\\\Leftrightarrow & \color{red}{23}x & = &-9\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-9}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{23} } & & \\ & V = \left\{ \frac{-9}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{-9}& = & -2 \color{red}{ -12x } \\\Leftrightarrow & -x \color{red}{-9}\color{blue}{+9+12x } & = & -2 \color{red}{ -12x }\color{blue}{+9+12x } \\\Leftrightarrow & -x \color{blue}{+12x } & = & -2 \color{blue}{+9} \\\Leftrightarrow &11x & = &7\\\Leftrightarrow & \color{red}{11}x & = &7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{+3}& = & 11 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{+3}\color{blue}{-3-14x } & = & 11 \color{red}{ +14x }\color{blue}{-3-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & 11 \color{blue}{-3} \\\Leftrightarrow &-25x & = &8\\\Leftrightarrow & \color{red}{-25}x & = &8\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{8}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{25} } & & \\ & V = \left\{ \frac{-8}{25} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{-12}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-12}\color{blue}{+12-x } & = & 7 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 7 \color{blue}{+12} \\\Leftrightarrow &-13x & = &19\\\Leftrightarrow & \color{red}{-13}x & = &19\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{19}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{13} } & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+12}& = & -8 \color{red}{ +14x } \\\Leftrightarrow & 13x \color{red}{+12}\color{blue}{-12-14x } & = & -8 \color{red}{ +14x }\color{blue}{-12-14x } \\\Leftrightarrow & 13x \color{blue}{-14x } & = & -8 \color{blue}{-12} \\\Leftrightarrow &-x & = &-20\\\Leftrightarrow & \color{red}{-}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-20}{-1} \\\Leftrightarrow & \color{green}{ x = 20 } & & \\ & V = \left\{ 20 \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{-6}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-6}\color{blue}{+6-x } & = & 7 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 7 \color{blue}{+6} \\\Leftrightarrow &-9x & = &13\\\Leftrightarrow & \color{red}{-9}x & = &13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{9} } & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{+6}& = & -5 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+6}\color{blue}{-6-x } & = & -5 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -5 \color{blue}{-6} \\\Leftrightarrow &11x & = &-11\\\Leftrightarrow & \color{red}{11}x & = &-11\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-11}{11} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{-15}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-15}\color{blue}{+15-x } & = & -10 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -10 \color{blue}{+15} \\\Leftrightarrow &-13x & = &5\\\Leftrightarrow & \color{red}{-13}x & = &5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)