Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{-15}& = & 15 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{-15}\color{blue}{+15+11x } & = & 15 \color{red}{ -11x }\color{blue}{+15+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & 15 \color{blue}{+15} \\\Leftrightarrow &14x & = &30\\\Leftrightarrow & \color{red}{14}x & = &30\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{30}{14} \\\Leftrightarrow & \color{green}{ x = \frac{15}{7} } & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{+1}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+1}\color{blue}{-1-x } & = & 6 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 6 \color{blue}{-1} \\\Leftrightarrow &-14x & = &5\\\Leftrightarrow & \color{red}{-14}x & = &5\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{5}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{14} } & & \\ & V = \left\{ \frac{-5}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{+15}& = & 9 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+15}\color{blue}{-15+13x } & = & 9 \color{red}{ -13x }\color{blue}{-15+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & 9 \color{blue}{-15} \\\Leftrightarrow &24x & = &-6\\\Leftrightarrow & \color{red}{24}x & = &-6\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-6}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{+9}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+9}\color{blue}{-9-x } & = & 14 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 14 \color{blue}{-9} \\\Leftrightarrow &-8x & = &5\\\Leftrightarrow & \color{red}{-8}x & = &5\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{5}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{-11}& = & -4 \color{red}{ +11x } \\\Leftrightarrow & 4x \color{red}{-11}\color{blue}{+11-11x } & = & -4 \color{red}{ +11x }\color{blue}{+11-11x } \\\Leftrightarrow & 4x \color{blue}{-11x } & = & -4 \color{blue}{+11} \\\Leftrightarrow &-7x & = &7\\\Leftrightarrow & \color{red}{-7}x & = &7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{7}{-7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{+14}& = & 12 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+14}\color{blue}{-14-5x } & = & 12 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & 12 \color{blue}{-14} \\\Leftrightarrow &-17x & = &-2\\\Leftrightarrow & \color{red}{-17}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-2}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{2}{17} } & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{-14}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-14}\color{blue}{+14-x } & = & 4 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 4 \color{blue}{+14} \\\Leftrightarrow &-8x & = &18\\\Leftrightarrow & \color{red}{-8}x & = &18\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{18}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{4} } & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{+15}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+15}\color{blue}{-15-13x } & = & 11 \color{red}{ +13x }\color{blue}{-15-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 11 \color{blue}{-15} \\\Leftrightarrow &-25x & = &-4\\\Leftrightarrow & \color{red}{-25}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-4}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{4}{25} } & & \\ & V = \left\{ \frac{4}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{-3}& = & -8 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{-3}\color{blue}{+3+3x } & = & -8 \color{red}{ -3x }\color{blue}{+3+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -8 \color{blue}{+3} \\\Leftrightarrow &7x & = &-5\\\Leftrightarrow & \color{red}{7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-5}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{-3}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-3}\color{blue}{+3-7x } & = & 13 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 13 \color{blue}{+3} \\\Leftrightarrow &-20x & = &16\\\Leftrightarrow & \color{red}{-20}x & = &16\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{16}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{-4}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & -x \color{red}{-4}\color{blue}{+4-13x } & = & 14 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & -x \color{blue}{-13x } & = & 14 \color{blue}{+4} \\\Leftrightarrow &-14x & = &18\\\Leftrightarrow & \color{red}{-14}x & = &18\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{18}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{+4}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-x } & = & -13 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -13 \color{blue}{-4} \\\Leftrightarrow &-14x & = &-17\\\Leftrightarrow & \color{red}{-14}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-17}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{17}{14} } & & \\ & V = \left\{ \frac{17}{14} \right\} & \\\end{align}\)