Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (2x+1)& = & 15 \color{red}{+} (-8-3x) \\\Leftrightarrow & 4x+2& = &15-8-3x \\\Leftrightarrow & 4x \color{red}{+2} & = &7 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+2} \color{blue}{-2} \color{blue}{+3x} & = &7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-2} \\\Leftrightarrow & 4x+3x& = &7-2 \\\Leftrightarrow & 7x& = &5 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{5}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{5}{7} & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-5x-4)& = & 12 \color{red}{-} (-15+x) \\\Leftrightarrow & -20x-16& = &12+15-x \\\Leftrightarrow & -20x \color{red}{-16} & = &27 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &27 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & -20x+x& = &27+16 \\\Leftrightarrow & -19x& = &43 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{43}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-43}{19} & & \\ & V = \left\{ \frac{-43}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (4x+5)& = & -6 \color{red}{+} (8-5x) \\\Leftrightarrow & 16x+20& = &-6+8-5x \\\Leftrightarrow & 16x \color{red}{+20} & = &2 \color{red}{-5x} \\\Leftrightarrow & 16x \color{red}{+20} \color{blue}{-20} \color{blue}{+5x} & = &2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-20} \\\Leftrightarrow & 16x+5x& = &2-20 \\\Leftrightarrow & 21x& = &-18 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-18}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-6}{7} & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-3x+6)& = & 6 \color{red}{-} (-12+x) \\\Leftrightarrow & -12x+24& = &6+12-x \\\Leftrightarrow & -12x \color{red}{+24} & = &18 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -12x+x& = &18-24 \\\Leftrightarrow & -11x& = &-6 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-6}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{6}{11} & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (6x-7)& = & 6 \color{red}{+} (-8+x) \\\Leftrightarrow & 12x-14& = &6-8+x \\\Leftrightarrow & 12x \color{red}{-14} & = &-2 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & 12x-x& = &-2+14 \\\Leftrightarrow & 11x& = &12 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{12}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{12}{11} & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (2x+2)& = & 7 \color{red}{-} (-2-3x) \\\Leftrightarrow & 10x+10& = &7+2+3x \\\Leftrightarrow & 10x \color{red}{+10} & = &9 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &9 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & 10x-3x& = &9-10 \\\Leftrightarrow & 7x& = &-1 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-1}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-2x+2)& = & 12 \color{red}{-} (-7+x) \\\Leftrightarrow & -12x+12& = &12+7-x \\\Leftrightarrow & -12x \color{red}{+12} & = &19 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &19 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -12x+x& = &19-12 \\\Leftrightarrow & -11x& = &7 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{7}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-7}{11} & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (x+6)& = & -14 \color{red}{-} (-15+x) \\\Leftrightarrow & 6x+36& = &-14+15-x \\\Leftrightarrow & 6x \color{red}{+36} & = &1 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & 6x+x& = &1-36 \\\Leftrightarrow & 7x& = &-35 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-35}{ \color{red}{7} } \\\Leftrightarrow & x = -5 & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-x+5)& = & 1 \color{red}{-} (-8-2x) \\\Leftrightarrow & -3x+15& = &1+8+2x \\\Leftrightarrow & -3x \color{red}{+15} & = &9 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{+15} \color{blue}{-15} \color{blue}{-2x} & = &9 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-15} \\\Leftrightarrow & -3x-2x& = &9-15 \\\Leftrightarrow & -5x& = &-6 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-6}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{6}{5} & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-4x+4)& = & -4 \color{red}{+} (3+x) \\\Leftrightarrow & -8x+8& = &-4+3+x \\\Leftrightarrow & -8x \color{red}{+8} & = &-1 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -8x-x& = &-1-8 \\\Leftrightarrow & -9x& = &-9 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-9}{ \color{red}{-9} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (6x-6)& = & 5 \color{red}{-} (2+x) \\\Leftrightarrow & 12x-12& = &5-2-x \\\Leftrightarrow & 12x \color{red}{-12} & = &3 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 12x+x& = &3+12 \\\Leftrightarrow & 13x& = &15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{15}{13} & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (6x-3)& = & 15 \color{red}{+} (4+x) \\\Leftrightarrow & 18x-9& = &15+4+x \\\Leftrightarrow & 18x \color{red}{-9} & = &19 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-9} \color{blue}{+9} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{+9} \\\Leftrightarrow & 18x-x& = &19+9 \\\Leftrightarrow & 17x& = &28 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{28}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{28}{17} & & \\ & V = \left\{ \frac{28}{17} \right\} & \\\end{align}\)