Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{+7}& = & 10 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+7}\color{blue}{-7+7x } & = & 10 \color{red}{ -7x }\color{blue}{-7+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 10 \color{blue}{-7} \\\Leftrightarrow &22x & = &3\\\Leftrightarrow & \color{red}{22}x & = &3\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{3}{22} \\\Leftrightarrow & \color{green}{ x = \frac{3}{22} } & & \\ & V = \left\{ \frac{3}{22} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{+14}& = & 9 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{+14}\color{blue}{-14-10x } & = & 9 \color{red}{ +10x }\color{blue}{-14-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & 9 \color{blue}{-14} \\\Leftrightarrow &-19x & = &-5\\\Leftrightarrow & \color{red}{-19}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-5}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{5}{19} } & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{-13}& = & 7 \color{red}{ +13x } \\\Leftrightarrow & 2x \color{red}{-13}\color{blue}{+13-13x } & = & 7 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & 2x \color{blue}{-13x } & = & 7 \color{blue}{+13} \\\Leftrightarrow &-11x & = &20\\\Leftrightarrow & \color{red}{-11}x & = &20\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{20}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{11} } & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{+2}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+2}\color{blue}{-2-x } & = & -11 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -11 \color{blue}{-2} \\\Leftrightarrow &-10x & = &-13\\\Leftrightarrow & \color{red}{-10}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-13}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{13}{10} } & & \\ & V = \left\{ \frac{13}{10} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{+11}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+11}\color{blue}{-11-x } & = & 9 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 9 \color{blue}{-11} \\\Leftrightarrow &-8x & = &-2\\\Leftrightarrow & \color{red}{-8}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{-9}& = & 14 \color{red}{ -3x } \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9+3x } & = & 14 \color{red}{ -3x }\color{blue}{+9+3x } \\\Leftrightarrow & x \color{blue}{+3x } & = & 14 \color{blue}{+9} \\\Leftrightarrow &4x & = &23\\\Leftrightarrow & \color{red}{4}x & = &23\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{23}{4} \\\Leftrightarrow & \color{green}{ x = \frac{23}{4} } & & \\ & V = \left\{ \frac{23}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{-3}& = & -2 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-3}\color{blue}{+3+6x } & = & -2 \color{red}{ -6x }\color{blue}{+3+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -2 \color{blue}{+3} \\\Leftrightarrow &19x & = &1\\\Leftrightarrow & \color{red}{19}x & = &1\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{1}{19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+8}& = & -5 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{+8}\color{blue}{-8-9x } & = & -5 \color{red}{ +9x }\color{blue}{-8-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & -5 \color{blue}{-8} \\\Leftrightarrow &-20x & = &-13\\\Leftrightarrow & \color{red}{-20}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-13}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{13}{20} } & & \\ & V = \left\{ \frac{13}{20} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{+2}& = & -11 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+2}\color{blue}{-2+3x } & = & -11 \color{red}{ -3x }\color{blue}{-2+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -11 \color{blue}{-2} \\\Leftrightarrow &13x & = &-13\\\Leftrightarrow & \color{red}{13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-13}{13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{+1}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+1}\color{blue}{-1-13x } & = & -5 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -5 \color{blue}{-1} \\\Leftrightarrow &-19x & = &-6\\\Leftrightarrow & \color{red}{-19}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-6}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{6}{19} } & & \\ & V = \left\{ \frac{6}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{-4}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-4}\color{blue}{+4-x } & = & -6 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -6 \color{blue}{+4} \\\Leftrightarrow &-9x & = &-2\\\Leftrightarrow & \color{red}{-9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{-15}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-15}\color{blue}{+15-x } & = & -5 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -5 \color{blue}{+15} \\\Leftrightarrow &-16x & = &10\\\Leftrightarrow & \color{red}{-16}x & = &10\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{10}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)