Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{-15}& = & -15 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{-15}\color{blue}{+15-4x } & = & -15 \color{red}{ +4x }\color{blue}{+15-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & -15 \color{blue}{+15} \\\Leftrightarrow &11x & = &0\\\Leftrightarrow & \color{red}{11}x & = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-9}& = & 14 \color{red}{ +8x } \\\Leftrightarrow & 3x \color{red}{-9}\color{blue}{+9-8x } & = & 14 \color{red}{ +8x }\color{blue}{+9-8x } \\\Leftrightarrow & 3x \color{blue}{-8x } & = & 14 \color{blue}{+9} \\\Leftrightarrow &-5x & = &23\\\Leftrightarrow & \color{red}{-5}x & = &23\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{23}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{5} } & & \\ & V = \left\{ \frac{-23}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{+11}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+11}\color{blue}{-11-x } & = & 9 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 9 \color{blue}{-11} \\\Leftrightarrow &-13x & = &-2\\\Leftrightarrow & \color{red}{-13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{-2}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-2}\color{blue}{+2-x } & = & -14 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -14 \color{blue}{+2} \\\Leftrightarrow &-6x & = &-12\\\Leftrightarrow & \color{red}{-6}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-12}{-6} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{-2}& = & -14 \color{red}{ +6x } \\\Leftrightarrow & x \color{red}{-2}\color{blue}{+2-6x } & = & -14 \color{red}{ +6x }\color{blue}{+2-6x } \\\Leftrightarrow & x \color{blue}{-6x } & = & -14 \color{blue}{+2} \\\Leftrightarrow &-5x & = &-12\\\Leftrightarrow & \color{red}{-5}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{-7}& = & 10 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{-7}\color{blue}{+7-4x } & = & 10 \color{red}{ +4x }\color{blue}{+7-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & 10 \color{blue}{+7} \\\Leftrightarrow &5x & = &17\\\Leftrightarrow & \color{red}{5}x & = &17\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{17}{5} \\\Leftrightarrow & \color{green}{ x = \frac{17}{5} } & & \\ & V = \left\{ \frac{17}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{-3}& = & -5 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{-3}\color{blue}{+3-14x } & = & -5 \color{red}{ +14x }\color{blue}{+3-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & -5 \color{blue}{+3} \\\Leftrightarrow &-25x & = &-2\\\Leftrightarrow & \color{red}{-25}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-2}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{2}{25} } & & \\ & V = \left\{ \frac{2}{25} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+3}& = & 2 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{+3}\color{blue}{-3-9x } & = & 2 \color{red}{ +9x }\color{blue}{-3-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & 2 \color{blue}{-3} \\\Leftrightarrow &-20x & = &-1\\\Leftrightarrow & \color{red}{-20}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-1}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{1}{20} } & & \\ & V = \left\{ \frac{1}{20} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{-8}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-8}\color{blue}{+8-x } & = & -13 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -13 \color{blue}{+8} \\\Leftrightarrow &-16x & = &-5\\\Leftrightarrow & \color{red}{-16}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-5}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{16} } & & \\ & V = \left\{ \frac{5}{16} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{-11}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-11}\color{blue}{+11-x } & = & -4 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -4 \color{blue}{+11} \\\Leftrightarrow &-3x & = &7\\\Leftrightarrow & \color{red}{-3}x & = &7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{+14}& = & -11 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14-7x } & = & -11 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -11 \color{blue}{-14} \\\Leftrightarrow &-20x & = &-25\\\Leftrightarrow & \color{red}{-20}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-25}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{+7}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+7}\color{blue}{-7-x } & = & -15 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -15 \color{blue}{-7} \\\Leftrightarrow &-16x & = &-22\\\Leftrightarrow & \color{red}{-16}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-22}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{11}{8} } & & \\ & V = \left\{ \frac{11}{8} \right\} & \\\end{align}\)