Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{+7}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{+7}\color{blue}{-7-13x } & = & -9 \color{red}{ +13x }\color{blue}{-7-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & -9 \color{blue}{-7} \\\Leftrightarrow &-15x & = &-16\\\Leftrightarrow & \color{red}{-15}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-16}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{16}{15} } & & \\ & V = \left\{ \frac{16}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-9}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-9}\color{blue}{+9-x } & = & 6 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 6 \color{blue}{+9} \\\Leftrightarrow &5x & = &15\\\Leftrightarrow & \color{red}{5}x & = &15\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{15}{5} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+10}& = & -1 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+10}\color{blue}{-10+11x } & = & -1 \color{red}{ -11x }\color{blue}{-10+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & -1 \color{blue}{-10} \\\Leftrightarrow &15x & = &-11\\\Leftrightarrow & \color{red}{15}x & = &-11\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-11}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{15} } & & \\ & V = \left\{ \frac{-11}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{+10}& = & 4 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+10}\color{blue}{-10+13x } & = & 4 \color{red}{ -13x }\color{blue}{-10+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 4 \color{blue}{-10} \\\Leftrightarrow &27x & = &-6\\\Leftrightarrow & \color{red}{27}x & = &-6\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-6}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{-7}& = & 5 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-7}\color{blue}{+7-x } & = & 5 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 5 \color{blue}{+7} \\\Leftrightarrow &7x & = &12\\\Leftrightarrow & \color{red}{7}x & = &12\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{12}{7} \\\Leftrightarrow & \color{green}{ x = \frac{12}{7} } & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{-10}& = & 2 \color{red}{ -3x } \\\Leftrightarrow & 13x \color{red}{-10}\color{blue}{+10+3x } & = & 2 \color{red}{ -3x }\color{blue}{+10+3x } \\\Leftrightarrow & 13x \color{blue}{+3x } & = & 2 \color{blue}{+10} \\\Leftrightarrow &16x & = &12\\\Leftrightarrow & \color{red}{16}x & = &12\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{12}{16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{-4}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-4}\color{blue}{+4-x } & = & -13 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -13 \color{blue}{+4} \\\Leftrightarrow &-3x & = &-9\\\Leftrightarrow & \color{red}{-3}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-9}{-3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+12}& = & 5 \color{red}{ +9x } \\\Leftrightarrow & 2x \color{red}{+12}\color{blue}{-12-9x } & = & 5 \color{red}{ +9x }\color{blue}{-12-9x } \\\Leftrightarrow & 2x \color{blue}{-9x } & = & 5 \color{blue}{-12} \\\Leftrightarrow &-7x & = &-7\\\Leftrightarrow & \color{red}{-7}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-7}{-7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{-6}& = & -9 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-6}\color{blue}{+6+11x } & = & -9 \color{red}{ -11x }\color{blue}{+6+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -9 \color{blue}{+6} \\\Leftrightarrow &17x & = &-3\\\Leftrightarrow & \color{red}{17}x & = &-3\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-3}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{17} } & & \\ & V = \left\{ \frac{-3}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+5}& = & -15 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{+5}\color{blue}{-5-8x } & = & -15 \color{red}{ +8x }\color{blue}{-5-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -15 \color{blue}{-5} \\\Leftrightarrow &-23x & = &-20\\\Leftrightarrow & \color{red}{-23}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-20}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{20}{23} } & & \\ & V = \left\{ \frac{20}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{+10}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+10}\color{blue}{-10-x } & = & -5 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -5 \color{blue}{-10} \\\Leftrightarrow &-16x & = &-15\\\Leftrightarrow & \color{red}{-16}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-15}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{15}{16} } & & \\ & V = \left\{ \frac{15}{16} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{-3}& = & 5 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-3}\color{blue}{+3-14x } & = & 5 \color{red}{ +14x }\color{blue}{+3-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 5 \color{blue}{+3} \\\Leftrightarrow &-27x & = &8\\\Leftrightarrow & \color{red}{-27}x & = &8\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{8}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{27} } & & \\ & V = \left\{ \frac{-8}{27} \right\} & \\\end{align}\)