Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(x+2=15-13x\)
2. \(-13x+11=-3+x\)
3. \(-10x-15=11+x\)
4. \(-3x-7=-2+x\)
5. \(6x+11=6+13x\)
6. \(x-12=-5+0x\)
7. \(-3x+11=2+4x\)
8. \(9x-4=8+x\)
9. \(13x-8=2+11x\)
10. \(-9x+8=2+10x\)
11. \(-2x-14=4+x\)
12. \(9x+7=7+13x\)

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{+2}& = & 15 \color{red}{ -13x } \\\Leftrightarrow & x \color{red}{+2}\color{blue}{-2+13x } & = & 15 \color{red}{ -13x }\color{blue}{-2+13x } \\\Leftrightarrow & x \color{blue}{+13x } & = & 15 \color{blue}{-2} \\\Leftrightarrow &14x & = &13\\\Leftrightarrow & \color{red}{14}x & = &13\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{13}{14} \\\Leftrightarrow & \color{green}{ x = \frac{13}{14} } & & \\ & V = \left\{ \frac{13}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{+11}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+11}\color{blue}{-11-x } & = & -3 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -3 \color{blue}{-11} \\\Leftrightarrow &-14x & = &-14\\\Leftrightarrow & \color{red}{-14}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-14}{-14} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{-15}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-15}\color{blue}{+15-x } & = & 11 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 11 \color{blue}{+15} \\\Leftrightarrow &-11x & = &26\\\Leftrightarrow & \color{red}{-11}x & = &26\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{26}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{11} } & & \\ & V = \left\{ \frac{-26}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{-7}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-7}\color{blue}{+7-x } & = & -2 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -2 \color{blue}{+7} \\\Leftrightarrow &-4x & = &5\\\Leftrightarrow & \color{red}{-4}x & = &5\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{5}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{+11}& = & 6 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{+11}\color{blue}{-11-13x } & = & 6 \color{red}{ +13x }\color{blue}{-11-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & 6 \color{blue}{-11} \\\Leftrightarrow &-7x & = &-5\\\Leftrightarrow & \color{red}{-7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{-12}& = & -5 \color{red}{ +0x } \\\Leftrightarrow & x \color{red}{-12}\color{blue}{+12+0x } & = & -5 \color{red}{ +0x }\color{blue}{+12+0x } \\\Leftrightarrow & x \color{blue}{+0x } & = & -5 \color{blue}{+12} \\\Leftrightarrow &x & = &7\\\Leftrightarrow & \color{red}{}x & = &7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 7 \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{+11}& = & 2 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{+11}\color{blue}{-11-4x } & = & 2 \color{red}{ +4x }\color{blue}{-11-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & 2 \color{blue}{-11} \\\Leftrightarrow &-7x & = &-9\\\Leftrightarrow & \color{red}{-7}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-4}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{-4}\color{blue}{+4-x } & = & 8 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & 8 \color{blue}{+4} \\\Leftrightarrow &8x & = &12\\\Leftrightarrow & \color{red}{8}x & = &12\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{12}{8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{-8}& = & 2 \color{red}{ +11x } \\\Leftrightarrow & 13x \color{red}{-8}\color{blue}{+8-11x } & = & 2 \color{red}{ +11x }\color{blue}{+8-11x } \\\Leftrightarrow & 13x \color{blue}{-11x } & = & 2 \color{blue}{+8} \\\Leftrightarrow &2x & = &10\\\Leftrightarrow & \color{red}{2}x & = &10\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{10}{2} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{+8}& = & 2 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{+8}\color{blue}{-8-10x } & = & 2 \color{red}{ +10x }\color{blue}{-8-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & 2 \color{blue}{-8} \\\Leftrightarrow &-19x & = &-6\\\Leftrightarrow & \color{red}{-19}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-6}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{6}{19} } & & \\ & V = \left\{ \frac{6}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{-14}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-14}\color{blue}{+14-x } & = & 4 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 4 \color{blue}{+14} \\\Leftrightarrow &-3x & = &18\\\Leftrightarrow & \color{red}{-3}x & = &18\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{18}{-3} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{+7}& = & 7 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{+7}\color{blue}{-7-13x } & = & 7 \color{red}{ +13x }\color{blue}{-7-13x } \\\Leftrightarrow & 9x \color{blue}{-13x } & = & 7 \color{blue}{-7} \\\Leftrightarrow &-4x & = &0\\\Leftrightarrow & \color{red}{-4}x & = &0\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{0}{-4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)