Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{+15}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & 6x \color{red}{+15}\color{blue}{-15-7x } & = & -7 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & 6x \color{blue}{-7x } & = & -7 \color{blue}{-15} \\\Leftrightarrow &-x & = &-22\\\Leftrightarrow & \color{red}{-}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-22}{-1} \\\Leftrightarrow & \color{green}{ x = 22 } & & \\ & V = \left\{ 22 \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{+14}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14-7x } & = & -1 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -1 \color{blue}{-14} \\\Leftrightarrow &-20x & = &-15\\\Leftrightarrow & \color{red}{-20}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-15}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{-11}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11-x } & = & -15 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -15 \color{blue}{+11} \\\Leftrightarrow &-6x & = &-4\\\Leftrightarrow & \color{red}{-6}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-4}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{+7}& = & 2 \color{red}{ +11x } \\\Leftrightarrow & 4x \color{red}{+7}\color{blue}{-7-11x } & = & 2 \color{red}{ +11x }\color{blue}{-7-11x } \\\Leftrightarrow & 4x \color{blue}{-11x } & = & 2 \color{blue}{-7} \\\Leftrightarrow &-7x & = &-5\\\Leftrightarrow & \color{red}{-7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{+4}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+4}\color{blue}{-4-x } & = & -2 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -2 \color{blue}{-4} \\\Leftrightarrow &-12x & = &-6\\\Leftrightarrow & \color{red}{-12}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-6}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{-13}& = & -9 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{-13}\color{blue}{+13-10x } & = & -9 \color{red}{ +10x }\color{blue}{+13-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & -9 \color{blue}{+13} \\\Leftrightarrow &-19x & = &4\\\Leftrightarrow & \color{red}{-19}x & = &4\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{4}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{19} } & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{+1}& = & 12 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+1}\color{blue}{-1+13x } & = & 12 \color{red}{ -13x }\color{blue}{-1+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & 12 \color{blue}{-1} \\\Leftrightarrow &22x & = &11\\\Leftrightarrow & \color{red}{22}x & = &11\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{11}{22} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{-1}& = & 13 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-1}\color{blue}{+1-9x } & = & 13 \color{red}{ +9x }\color{blue}{+1-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 13 \color{blue}{+1} \\\Leftrightarrow &-17x & = &14\\\Leftrightarrow & \color{red}{-17}x & = &14\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{14}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{17} } & & \\ & V = \left\{ \frac{-14}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+5}& = & -3 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+5}\color{blue}{-5+2x } & = & -3 \color{red}{ -2x }\color{blue}{-5+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -3 \color{blue}{-5} \\\Leftrightarrow &17x & = &-8\\\Leftrightarrow & \color{red}{17}x & = &-8\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-8}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{17} } & & \\ & V = \left\{ \frac{-8}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{+12}& = & 9 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{+12}\color{blue}{-12-6x } & = & 9 \color{red}{ +6x }\color{blue}{-12-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & 9 \color{blue}{-12} \\\Leftrightarrow &-x & = &-3\\\Leftrightarrow & \color{red}{-}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-3}{-1} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{+15}& = & -4 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+15}\color{blue}{-15-9x } & = & -4 \color{red}{ +9x }\color{blue}{-15-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -4 \color{blue}{-15} \\\Leftrightarrow &-17x & = &-19\\\Leftrightarrow & \color{red}{-17}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-19}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{19}{17} } & & \\ & V = \left\{ \frac{19}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{+5}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{+5}\color{blue}{-5-x } & = & -13 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -13 \color{blue}{-5} \\\Leftrightarrow &3x & = &-18\\\Leftrightarrow & \color{red}{3}x & = &-18\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-18}{3} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)