Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{-3}& = & -11 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-3}\color{blue}{+3+13x } & = & -11 \color{red}{ -13x }\color{blue}{+3+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & -11 \color{blue}{+3} \\\Leftrightarrow &22x & = &-8\\\Leftrightarrow & \color{red}{22}x & = &-8\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-8}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+7}& = & -10 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{+7}\color{blue}{-7+13x } & = & -10 \color{red}{ -13x }\color{blue}{-7+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & -10 \color{blue}{-7} \\\Leftrightarrow &21x & = &-17\\\Leftrightarrow & \color{red}{21}x & = &-17\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-17}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{21} } & & \\ & V = \left\{ \frac{-17}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{+2}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+2}\color{blue}{-2-x } & = & -12 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -12 \color{blue}{-2} \\\Leftrightarrow &-13x & = &-14\\\Leftrightarrow & \color{red}{-13}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-14}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{14}{13} } & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{+1}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+1}\color{blue}{-1-x } & = & 15 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 15 \color{blue}{-1} \\\Leftrightarrow &-15x & = &14\\\Leftrightarrow & \color{red}{-15}x & = &14\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{14}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{15} } & & \\ & V = \left\{ \frac{-14}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{+3}& = & -2 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{+3}\color{blue}{-3-4x } & = & -2 \color{red}{ +4x }\color{blue}{-3-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & -2 \color{blue}{-3} \\\Leftrightarrow &5x & = &-5\\\Leftrightarrow & \color{red}{5}x & = &-5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-5}{5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{+4}& = & 4 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{+4}\color{blue}{-4+8x } & = & 4 \color{red}{ -8x }\color{blue}{-4+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & 4 \color{blue}{-4} \\\Leftrightarrow &11x & = &0\\\Leftrightarrow & \color{red}{11}x & = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{-8}& = & 6 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{-8}\color{blue}{+8+8x } & = & 6 \color{red}{ -8x }\color{blue}{+8+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & 6 \color{blue}{+8} \\\Leftrightarrow &17x & = &14\\\Leftrightarrow & \color{red}{17}x & = &14\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{14}{17} \\\Leftrightarrow & \color{green}{ x = \frac{14}{17} } & & \\ & V = \left\{ \frac{14}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{-2}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-2}\color{blue}{+2-x } & = & -12 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -12 \color{blue}{+2} \\\Leftrightarrow &-9x & = &-10\\\Leftrightarrow & \color{red}{-9}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-10}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{10}{9} } & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{+7}& = & 2 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{+7}\color{blue}{-7+2x } & = & 2 \color{red}{ -2x }\color{blue}{-7+2x } \\\Leftrightarrow & 5x \color{blue}{+2x } & = & 2 \color{blue}{-7} \\\Leftrightarrow &7x & = &-5\\\Leftrightarrow & \color{red}{7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-5}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{-3}& = & 2 \color{red}{ +2x } \\\Leftrightarrow & -x \color{red}{-3}\color{blue}{+3-2x } & = & 2 \color{red}{ +2x }\color{blue}{+3-2x } \\\Leftrightarrow & -x \color{blue}{-2x } & = & 2 \color{blue}{+3} \\\Leftrightarrow &-3x & = &5\\\Leftrightarrow & \color{red}{-3}x & = &5\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{5}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-9}& = & 11 \color{red}{ +10x } \\\Leftrightarrow & 7x \color{red}{-9}\color{blue}{+9-10x } & = & 11 \color{red}{ +10x }\color{blue}{+9-10x } \\\Leftrightarrow & 7x \color{blue}{-10x } & = & 11 \color{blue}{+9} \\\Leftrightarrow &-3x & = &20\\\Leftrightarrow & \color{red}{-3}x & = &20\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{20}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{3} } & & \\ & V = \left\{ \frac{-20}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{-15}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-15}\color{blue}{+15-x } & = & -1 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -1 \color{blue}{+15} \\\Leftrightarrow &-16x & = &14\\\Leftrightarrow & \color{red}{-16}x & = &14\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{14}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{8} } & & \\ & V = \left\{ \frac{-7}{8} \right\} & \\\end{align}\)