Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{+14}& = & -3 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14-4x } & = & -3 \color{red}{ +4x }\color{blue}{-14-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & -3 \color{blue}{-14} \\\Leftrightarrow &-11x & = &-17\\\Leftrightarrow & \color{red}{-11}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-17}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{17}{11} } & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{+15}& = & 6 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+15}\color{blue}{-15-11x } & = & 6 \color{red}{ +11x }\color{blue}{-15-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & 6 \color{blue}{-15} \\\Leftrightarrow &-5x & = &-9\\\Leftrightarrow & \color{red}{-5}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{-9}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-9}\color{blue}{+9-x } & = & 3 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 3 \color{blue}{+9} \\\Leftrightarrow &-9x & = &12\\\Leftrightarrow & \color{red}{-9}x & = &12\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{12}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{-10}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-10}\color{blue}{+10-x } & = & 9 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 9 \color{blue}{+10} \\\Leftrightarrow &-3x & = &19\\\Leftrightarrow & \color{red}{-3}x & = &19\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{19}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{3} } & & \\ & V = \left\{ \frac{-19}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{-3}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-3}\color{blue}{+3-x } & = & 14 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 14 \color{blue}{+3} \\\Leftrightarrow &-11x & = &17\\\Leftrightarrow & \color{red}{-11}x & = &17\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{17}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{11} } & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{+9}& = & 9 \color{red}{ +11x } \\\Leftrightarrow & 9x \color{red}{+9}\color{blue}{-9-11x } & = & 9 \color{red}{ +11x }\color{blue}{-9-11x } \\\Leftrightarrow & 9x \color{blue}{-11x } & = & 9 \color{blue}{-9} \\\Leftrightarrow &-2x & = &0\\\Leftrightarrow & \color{red}{-2}x & = &0\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{0}{-2} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{-3}& = & 12 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-3}\color{blue}{+3-9x } & = & 12 \color{red}{ +9x }\color{blue}{+3-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & 12 \color{blue}{+3} \\\Leftrightarrow &-13x & = &15\\\Leftrightarrow & \color{red}{-13}x & = &15\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{15}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{13} } & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{+3}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+3}\color{blue}{-3-x } & = & -7 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -7 \color{blue}{-3} \\\Leftrightarrow &-15x & = &-10\\\Leftrightarrow & \color{red}{-15}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-10}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{+1}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+1}\color{blue}{-1-x } & = & 2 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 2 \color{blue}{-1} \\\Leftrightarrow &-13x & = &1\\\Leftrightarrow & \color{red}{-13}x & = &1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{-2}& = & 11 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{-2}\color{blue}{+2+11x } & = & 11 \color{red}{ -11x }\color{blue}{+2+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & 11 \color{blue}{+2} \\\Leftrightarrow &20x & = &13\\\Leftrightarrow & \color{red}{20}x & = &13\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{13}{20} \\\Leftrightarrow & \color{green}{ x = \frac{13}{20} } & & \\ & V = \left\{ \frac{13}{20} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{-1}& = & 4 \color{red}{ +9x } \\\Leftrightarrow & x \color{red}{-1}\color{blue}{+1-9x } & = & 4 \color{red}{ +9x }\color{blue}{+1-9x } \\\Leftrightarrow & x \color{blue}{-9x } & = & 4 \color{blue}{+1} \\\Leftrightarrow &-8x & = &5\\\Leftrightarrow & \color{red}{-8}x & = &5\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{5}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{-12}& = & -10 \color{red}{ +12x } \\\Leftrightarrow & x \color{red}{-12}\color{blue}{+12-12x } & = & -10 \color{red}{ +12x }\color{blue}{+12-12x } \\\Leftrightarrow & x \color{blue}{-12x } & = & -10 \color{blue}{+12} \\\Leftrightarrow &-11x & = &2\\\Leftrightarrow & \color{red}{-11}x & = &2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)