Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{+4}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+4}\color{blue}{-4-x } & = & -14 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -14 \color{blue}{-4} \\\Leftrightarrow &-15x & = &-18\\\Leftrightarrow & \color{red}{-15}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-18}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{+13}& = & -2 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{+13}\color{blue}{-13+14x } & = & -2 \color{red}{ -14x }\color{blue}{-13+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & -2 \color{blue}{-13} \\\Leftrightarrow &17x & = &-15\\\Leftrightarrow & \color{red}{17}x & = &-15\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-15}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{17} } & & \\ & V = \left\{ \frac{-15}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{-11}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-11}\color{blue}{+11-11x } & = & 12 \color{red}{ +11x }\color{blue}{+11-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & 12 \color{blue}{+11} \\\Leftrightarrow &-5x & = &23\\\Leftrightarrow & \color{red}{-5}x & = &23\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{23}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{5} } & & \\ & V = \left\{ \frac{-23}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{+4}& = & -11 \color{red}{ +11x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-11x } & = & -11 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & -13x \color{blue}{-11x } & = & -11 \color{blue}{-4} \\\Leftrightarrow &-24x & = &-15\\\Leftrightarrow & \color{red}{-24}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-24}x}{ \color{blue}{ -24}} & = & \frac{-15}{-24} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{-4}& = & 10 \color{red}{ +5x } \\\Leftrightarrow & 11x \color{red}{-4}\color{blue}{+4-5x } & = & 10 \color{red}{ +5x }\color{blue}{+4-5x } \\\Leftrightarrow & 11x \color{blue}{-5x } & = & 10 \color{blue}{+4} \\\Leftrightarrow &6x & = &14\\\Leftrightarrow & \color{red}{6}x & = &14\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{14}{6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{-10}& = & 7 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-10}\color{blue}{+10-11x } & = & 7 \color{red}{ +11x }\color{blue}{+10-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & 7 \color{blue}{+10} \\\Leftrightarrow &x & = &17\\\Leftrightarrow & \color{red}{}x & = &17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 17 \\\Leftrightarrow & \color{green}{ x = 17 } & & \\ & V = \left\{ 17 \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{-7}& = & 11 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-7}\color{blue}{+7+8x } & = & 11 \color{red}{ -8x }\color{blue}{+7+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & 11 \color{blue}{+7} \\\Leftrightarrow &11x & = &18\\\Leftrightarrow & \color{red}{11}x & = &18\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{18}{11} \\\Leftrightarrow & \color{green}{ x = \frac{18}{11} } & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{-15}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-15}\color{blue}{+15-x } & = & 7 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 7 \color{blue}{+15} \\\Leftrightarrow &-13x & = &22\\\Leftrightarrow & \color{red}{-13}x & = &22\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{22}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{13} } & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{-7}& = & -1 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-7}\color{blue}{+7+7x } & = & -1 \color{red}{ -7x }\color{blue}{+7+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & -1 \color{blue}{+7} \\\Leftrightarrow &11x & = &6\\\Leftrightarrow & \color{red}{11}x & = &6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{+5}& = & -13 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+5}\color{blue}{-5+3x } & = & -13 \color{red}{ -3x }\color{blue}{-5+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -13 \color{blue}{-5} \\\Leftrightarrow &13x & = &-18\\\Leftrightarrow & \color{red}{13}x & = &-18\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-18}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{13} } & & \\ & V = \left\{ \frac{-18}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{+2}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{+2}\color{blue}{-2-x } & = & -6 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -6 \color{blue}{-2} \\\Leftrightarrow &3x & = &-8\\\Leftrightarrow & \color{red}{3}x & = &-8\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-8}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{+5}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+5}\color{blue}{-5-x } & = & -7 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -7 \color{blue}{-5} \\\Leftrightarrow &7x & = &-12\\\Leftrightarrow & \color{red}{7}x & = &-12\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-12}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)