Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{-1}& = & 4 \color{red}{ +3x } \\\Leftrightarrow & 14x \color{red}{-1}\color{blue}{+1-3x } & = & 4 \color{red}{ +3x }\color{blue}{+1-3x } \\\Leftrightarrow & 14x \color{blue}{-3x } & = & 4 \color{blue}{+1} \\\Leftrightarrow &11x & = &5\\\Leftrightarrow & \color{red}{11}x & = &5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{+9}& = & -4 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+9}\color{blue}{-9-5x } & = & -4 \color{red}{ +5x }\color{blue}{-9-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -4 \color{blue}{-9} \\\Leftrightarrow &7x & = &-13\\\Leftrightarrow & \color{red}{7}x & = &-13\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-13}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{7} } & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{-10}& = & 14 \color{red}{ +10x } \\\Leftrightarrow & 3x \color{red}{-10}\color{blue}{+10-10x } & = & 14 \color{red}{ +10x }\color{blue}{+10-10x } \\\Leftrightarrow & 3x \color{blue}{-10x } & = & 14 \color{blue}{+10} \\\Leftrightarrow &-7x & = &24\\\Leftrightarrow & \color{red}{-7}x & = &24\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{24}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{7} } & & \\ & V = \left\{ \frac{-24}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{+10}& = & -3 \color{red}{ +10x } \\\Leftrightarrow & 11x \color{red}{+10}\color{blue}{-10-10x } & = & -3 \color{red}{ +10x }\color{blue}{-10-10x } \\\Leftrightarrow & 11x \color{blue}{-10x } & = & -3 \color{blue}{-10} \\\Leftrightarrow &x & = &-13\\\Leftrightarrow & \color{red}{}x & = &-13\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -13 \\\Leftrightarrow & \color{green}{ x = -13 } & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{-2}& = & -15 \color{red}{ +3x } \\\Leftrightarrow & 10x \color{red}{-2}\color{blue}{+2-3x } & = & -15 \color{red}{ +3x }\color{blue}{+2-3x } \\\Leftrightarrow & 10x \color{blue}{-3x } & = & -15 \color{blue}{+2} \\\Leftrightarrow &7x & = &-13\\\Leftrightarrow & \color{red}{7}x & = &-13\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-13}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{7} } & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{-5}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-5}\color{blue}{+5-x } & = & 9 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 9 \color{blue}{+5} \\\Leftrightarrow &-12x & = &14\\\Leftrightarrow & \color{red}{-12}x & = &14\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{14}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{-12}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-12}\color{blue}{+12-x } & = & -3 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -3 \color{blue}{+12} \\\Leftrightarrow &3x & = &9\\\Leftrightarrow & \color{red}{3}x & = &9\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{9}{3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{+2}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+2}\color{blue}{-2-13x } & = & 11 \color{red}{ +13x }\color{blue}{-2-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 11 \color{blue}{-2} \\\Leftrightarrow &-28x & = &9\\\Leftrightarrow & \color{red}{-28}x & = &9\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{9}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{28} } & & \\ & V = \left\{ \frac{-9}{28} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{+5}& = & 6 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{+5}\color{blue}{-5-11x } & = & 6 \color{red}{ +11x }\color{blue}{-5-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & 6 \color{blue}{-5} \\\Leftrightarrow &-16x & = &1\\\Leftrightarrow & \color{red}{-16}x & = &1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{16} } & & \\ & V = \left\{ \frac{-1}{16} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{-4}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-4}\color{blue}{+4-x } & = & -9 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -9 \color{blue}{+4} \\\Leftrightarrow &-3x & = &-5\\\Leftrightarrow & \color{red}{-3}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-5}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{+8}& = & -13 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{+8}\color{blue}{-8-9x } & = & -13 \color{red}{ +9x }\color{blue}{-8-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & -13 \color{blue}{-8} \\\Leftrightarrow &-20x & = &-21\\\Leftrightarrow & \color{red}{-20}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-21}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{21}{20} } & & \\ & V = \left\{ \frac{21}{20} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{+9}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+9}\color{blue}{-9-x } & = & -8 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -8 \color{blue}{-9} \\\Leftrightarrow &-8x & = &-17\\\Leftrightarrow & \color{red}{-8}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-17}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{17}{8} } & & \\ & V = \left\{ \frac{17}{8} \right\} & \\\end{align}\)