Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{-2}& = & 6 \color{red}{ +9x } \\\Leftrightarrow & 10x \color{red}{-2}\color{blue}{+2-9x } & = & 6 \color{red}{ +9x }\color{blue}{+2-9x } \\\Leftrightarrow & 10x \color{blue}{-9x } & = & 6 \color{blue}{+2} \\\Leftrightarrow &x & = &8\\\Leftrightarrow & \color{red}{}x & = &8\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 8 \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-14}& = & 11 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-14}\color{blue}{+14-9x } & = & 11 \color{red}{ +9x }\color{blue}{+14-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 11 \color{blue}{+14} \\\Leftrightarrow &-17x & = &25\\\Leftrightarrow & \color{red}{-17}x & = &25\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{25}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{17} } & & \\ & V = \left\{ \frac{-25}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{-1}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-1}\color{blue}{+1-x } & = & 7 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 7 \color{blue}{+1} \\\Leftrightarrow &-4x & = &8\\\Leftrightarrow & \color{red}{-4}x & = &8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{8}{-4} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{-12}& = & -5 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-12}\color{blue}{+12+6x } & = & -5 \color{red}{ -6x }\color{blue}{+12+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -5 \color{blue}{+12} \\\Leftrightarrow &19x & = &7\\\Leftrightarrow & \color{red}{19}x & = &7\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{7}{19} \\\Leftrightarrow & \color{green}{ x = \frac{7}{19} } & & \\ & V = \left\{ \frac{7}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{-3}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-3}\color{blue}{+3-x } & = & -10 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -10 \color{blue}{+3} \\\Leftrightarrow &-4x & = &-7\\\Leftrightarrow & \color{red}{-4}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-7}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{-11}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-11}\color{blue}{+11-x } & = & 14 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 14 \color{blue}{+11} \\\Leftrightarrow &-9x & = &25\\\Leftrightarrow & \color{red}{-9}x & = &25\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{25}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{9} } & & \\ & V = \left\{ \frac{-25}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{+7}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+7}\color{blue}{-7-x } & = & -10 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -10 \color{blue}{-7} \\\Leftrightarrow &-11x & = &-17\\\Leftrightarrow & \color{red}{-11}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-17}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{17}{11} } & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{-8}& = & -12 \color{red}{ -9x } \\\Leftrightarrow & -x \color{red}{-8}\color{blue}{+8+9x } & = & -12 \color{red}{ -9x }\color{blue}{+8+9x } \\\Leftrightarrow & -x \color{blue}{+9x } & = & -12 \color{blue}{+8} \\\Leftrightarrow &8x & = &-4\\\Leftrightarrow & \color{red}{8}x & = &-4\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-4}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{+7}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+7}\color{blue}{-7-13x } & = & 3 \color{red}{ +13x }\color{blue}{-7-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 3 \color{blue}{-7} \\\Leftrightarrow &-19x & = &-4\\\Leftrightarrow & \color{red}{-19}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-4}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{4}{19} } & & \\ & V = \left\{ \frac{4}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+1}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+1}\color{blue}{-1-x } & = & 6 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 6 \color{blue}{-1} \\\Leftrightarrow &-16x & = &5\\\Leftrightarrow & \color{red}{-16}x & = &5\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{5}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{16} } & & \\ & V = \left\{ \frac{-5}{16} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{-14}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-14}\color{blue}{+14-x } & = & -3 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -3 \color{blue}{+14} \\\Leftrightarrow &-8x & = &11\\\Leftrightarrow & \color{red}{-8}x & = &11\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{11}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{8} } & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{-3}& = & 15 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-3}\color{blue}{+3+11x } & = & 15 \color{red}{ -11x }\color{blue}{+3+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & 15 \color{blue}{+3} \\\Leftrightarrow &26x & = &18\\\Leftrightarrow & \color{red}{26}x & = &18\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{18}{26} \\\Leftrightarrow & \color{green}{ x = \frac{9}{13} } & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)