Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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