Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{-12}& = & -5 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{-12}\color{blue}{+12-10x } & = & -5 \color{red}{ +10x }\color{blue}{+12-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & -5 \color{blue}{+12} \\\Leftrightarrow &-x & = &7\\\Leftrightarrow & \color{red}{-}x & = &7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{7}{-1} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{-7}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-7}\color{blue}{+7-7x } & = & -4 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -4 \color{blue}{+7} \\\Leftrightarrow &-17x & = &3\\\Leftrightarrow & \color{red}{-17}x & = &3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{17} } & & \\ & V = \left\{ \frac{-3}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+9}& = & -9 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+9}\color{blue}{-9+13x } & = & -9 \color{red}{ -13x }\color{blue}{-9+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & -9 \color{blue}{-9} \\\Leftrightarrow &22x & = &-18\\\Leftrightarrow & \color{red}{22}x & = &-18\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-18}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{-10}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-10}\color{blue}{+10-x } & = & -8 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -8 \color{blue}{+10} \\\Leftrightarrow &-6x & = &2\\\Leftrightarrow & \color{red}{-6}x & = &2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-11}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-11}\color{blue}{+11-x } & = & 7 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 7 \color{blue}{+11} \\\Leftrightarrow &5x & = &18\\\Leftrightarrow & \color{red}{5}x & = &18\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{18}{5} \\\Leftrightarrow & \color{green}{ x = \frac{18}{5} } & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{+2}& = & -3 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{+2}\color{blue}{-2-8x } & = & -3 \color{red}{ +8x }\color{blue}{-2-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -3 \color{blue}{-2} \\\Leftrightarrow &-23x & = &-5\\\Leftrightarrow & \color{red}{-23}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-5}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{5}{23} } & & \\ & V = \left\{ \frac{5}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{-5}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & 7x \color{red}{-5}\color{blue}{+5-13x } & = & -13 \color{red}{ +13x }\color{blue}{+5-13x } \\\Leftrightarrow & 7x \color{blue}{-13x } & = & -13 \color{blue}{+5} \\\Leftrightarrow &-6x & = &-8\\\Leftrightarrow & \color{red}{-6}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-8}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{-5}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-5}\color{blue}{+5-x } & = & 12 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 12 \color{blue}{+5} \\\Leftrightarrow &-15x & = &17\\\Leftrightarrow & \color{red}{-15}x & = &17\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{17}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{15} } & & \\ & V = \left\{ \frac{-17}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+5}& = & -5 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{+5}\color{blue}{-5+12x } & = & -5 \color{red}{ -12x }\color{blue}{-5+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & -5 \color{blue}{-5} \\\Leftrightarrow &25x & = &-10\\\Leftrightarrow & \color{red}{25}x & = &-10\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-10}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{+11}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{+11}\color{blue}{-11-13x } & = & 5 \color{red}{ +13x }\color{blue}{-11-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & 5 \color{blue}{-11} \\\Leftrightarrow &-7x & = &-6\\\Leftrightarrow & \color{red}{-7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{-10}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-10}\color{blue}{+10-x } & = & 2 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 2 \color{blue}{+10} \\\Leftrightarrow &-9x & = &12\\\Leftrightarrow & \color{red}{-9}x & = &12\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{12}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{-5}& = & -15 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{-5}\color{blue}{+5-11x } & = & -15 \color{red}{ +11x }\color{blue}{+5-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & -15 \color{blue}{+5} \\\Leftrightarrow &-18x & = &-10\\\Leftrightarrow & \color{red}{-18}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-10}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)