Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{-12}& = & 2 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12+11x } & = & 2 \color{red}{ -11x }\color{blue}{+12+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & 2 \color{blue}{+12} \\\Leftrightarrow &14x & = &14\\\Leftrightarrow & \color{red}{14}x & = &14\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{14}{14} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+5}& = & -3 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+5}\color{blue}{-5+7x } & = & -3 \color{red}{ -7x }\color{blue}{-5+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -3 \color{blue}{-5} \\\Leftrightarrow &15x & = &-8\\\Leftrightarrow & \color{red}{15}x & = &-8\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-8}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{15} } & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{-4}& = & 5 \color{red}{ -9x } \\\Leftrightarrow & 7x \color{red}{-4}\color{blue}{+4+9x } & = & 5 \color{red}{ -9x }\color{blue}{+4+9x } \\\Leftrightarrow & 7x \color{blue}{+9x } & = & 5 \color{blue}{+4} \\\Leftrightarrow &16x & = &9\\\Leftrightarrow & \color{red}{16}x & = &9\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{9}{16} \\\Leftrightarrow & \color{green}{ x = \frac{9}{16} } & & \\ & V = \left\{ \frac{9}{16} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{+4}& = & -2 \color{red}{ +13x } \\\Leftrightarrow & 15x \color{red}{+4}\color{blue}{-4-13x } & = & -2 \color{red}{ +13x }\color{blue}{-4-13x } \\\Leftrightarrow & 15x \color{blue}{-13x } & = & -2 \color{blue}{-4} \\\Leftrightarrow &2x & = &-6\\\Leftrightarrow & \color{red}{2}x & = &-6\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-6}{2} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{+10}& = & -2 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+10}\color{blue}{-10-13x } & = & -2 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -2 \color{blue}{-10} \\\Leftrightarrow &-28x & = &-12\\\Leftrightarrow & \color{red}{-28}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-12}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{-15}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-15}\color{blue}{+15-7x } & = & -1 \color{red}{ +7x }\color{blue}{+15-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -1 \color{blue}{+15} \\\Leftrightarrow &-13x & = &14\\\Leftrightarrow & \color{red}{-13}x & = &14\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{14}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{13} } & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+6}& = & 5 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+6}\color{blue}{-6+7x } & = & 5 \color{red}{ -7x }\color{blue}{-6+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 5 \color{blue}{-6} \\\Leftrightarrow &19x & = &-1\\\Leftrightarrow & \color{red}{19}x & = &-1\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-1}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{19} } & & \\ & V = \left\{ \frac{-1}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{+4}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{+4}\color{blue}{-4-11x } & = & -3 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & -3 \color{blue}{-4} \\\Leftrightarrow &-18x & = &-7\\\Leftrightarrow & \color{red}{-18}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-7}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{7}{18} } & & \\ & V = \left\{ \frac{7}{18} \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{+6}& = & -7 \color{red}{ -15x } \\\Leftrightarrow & x \color{red}{+6}\color{blue}{-6+15x } & = & -7 \color{red}{ -15x }\color{blue}{-6+15x } \\\Leftrightarrow & x \color{blue}{+15x } & = & -7 \color{blue}{-6} \\\Leftrightarrow &16x & = &-13\\\Leftrightarrow & \color{red}{16}x & = &-13\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-13}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{16} } & & \\ & V = \left\{ \frac{-13}{16} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{-15}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-15}\color{blue}{+15-x } & = & -9 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -9 \color{blue}{+15} \\\Leftrightarrow &11x & = &6\\\Leftrightarrow & \color{red}{11}x & = &6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{+13}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+13}\color{blue}{-13-x } & = & 9 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 9 \color{blue}{-13} \\\Leftrightarrow &-15x & = &-4\\\Leftrightarrow & \color{red}{-15}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{-7}& = & -8 \color{red}{ -2x } \\\Leftrightarrow & x \color{red}{-7}\color{blue}{+7+2x } & = & -8 \color{red}{ -2x }\color{blue}{+7+2x } \\\Leftrightarrow & x \color{blue}{+2x } & = & -8 \color{blue}{+7} \\\Leftrightarrow &3x & = &-1\\\Leftrightarrow & \color{red}{3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-1}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)