Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{+11}& = & -10 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+11}\color{blue}{-11-7x } & = & -10 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -10 \color{blue}{-11} \\\Leftrightarrow &3x & = &-21\\\Leftrightarrow & \color{red}{3}x & = &-21\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-21}{3} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{-11}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-11}\color{blue}{+11-x } & = & -4 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -4 \color{blue}{+11} \\\Leftrightarrow &-15x & = &7\\\Leftrightarrow & \color{red}{-15}x & = &7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{15} } & & \\ & V = \left\{ \frac{-7}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{-15}& = & -11 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-15}\color{blue}{+15+3x } & = & -11 \color{red}{ -3x }\color{blue}{+15+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -11 \color{blue}{+15} \\\Leftrightarrow &13x & = &4\\\Leftrightarrow & \color{red}{13}x & = &4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-4}& = & 11 \color{red}{ +14x } \\\Leftrightarrow & 15x \color{red}{-4}\color{blue}{+4-14x } & = & 11 \color{red}{ +14x }\color{blue}{+4-14x } \\\Leftrightarrow & 15x \color{blue}{-14x } & = & 11 \color{blue}{+4} \\\Leftrightarrow &x & = &15\\\Leftrightarrow & \color{red}{}x & = &15\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 15 \\\Leftrightarrow & \color{green}{ x = 15 } & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{+1}& = & 6 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{+1}\color{blue}{-1-5x } & = & 6 \color{red}{ +5x }\color{blue}{-1-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & 6 \color{blue}{-1} \\\Leftrightarrow &-7x & = &5\\\Leftrightarrow & \color{red}{-7}x & = &5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{-14}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-14}\color{blue}{+14-x } & = & -2 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -2 \color{blue}{+14} \\\Leftrightarrow &5x & = &12\\\Leftrightarrow & \color{red}{5}x & = &12\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{12}{5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{+10}& = & 7 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{+10}\color{blue}{-10+2x } & = & 7 \color{red}{ -2x }\color{blue}{-10+2x } \\\Leftrightarrow & 5x \color{blue}{+2x } & = & 7 \color{blue}{-10} \\\Leftrightarrow &7x & = &-3\\\Leftrightarrow & \color{red}{7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-3}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{+13}& = & -4 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+13}\color{blue}{-13+5x } & = & -4 \color{red}{ -5x }\color{blue}{-13+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -4 \color{blue}{-13} \\\Leftrightarrow &11x & = &-17\\\Leftrightarrow & \color{red}{11}x & = &-17\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-17}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{11} } & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{+2}& = & 8 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{+2}\color{blue}{-2+8x } & = & 8 \color{red}{ -8x }\color{blue}{-2+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & 8 \color{blue}{-2} \\\Leftrightarrow &17x & = &6\\\Leftrightarrow & \color{red}{17}x & = &6\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{6}{17} \\\Leftrightarrow & \color{green}{ x = \frac{6}{17} } & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{+9}& = & 6 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{+9}\color{blue}{-9-13x } & = & 6 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & 6 \color{blue}{-9} \\\Leftrightarrow &-17x & = &-3\\\Leftrightarrow & \color{red}{-17}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{3}{17} } & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{-9}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-x } & = & -6 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -6 \color{blue}{+9} \\\Leftrightarrow &-6x & = &3\\\Leftrightarrow & \color{red}{-6}x & = &3\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{3}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{+2}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+2}\color{blue}{-2-x } & = & 4 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 4 \color{blue}{-2} \\\Leftrightarrow &-16x & = &2\\\Leftrightarrow & \color{red}{-16}x & = &2\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{2}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)