Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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