Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-4x+7)& = & 10 \color{red}{-} (-3+x) \\\Leftrightarrow & -8x+14& = &10+3-x \\\Leftrightarrow & -8x \color{red}{+14} & = &13 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & -8x+x& = &13-14 \\\Leftrightarrow & -7x& = &-1 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-1}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{1}{7} & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (6x+4)& = & 6 \color{red}{-} (-6+x) \\\Leftrightarrow & 30x+20& = &6+6-x \\\Leftrightarrow & 30x \color{red}{+20} & = &12 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 30x+x& = &12-20 \\\Leftrightarrow & 31x& = &-8 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-8}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-8}{31} & & \\ & V = \left\{ \frac{-8}{31} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-5x+6)& = & -8 \color{red}{-} (-14+x) \\\Leftrightarrow & -10x+12& = &-8+14-x \\\Leftrightarrow & -10x \color{red}{+12} & = &6 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -10x+x& = &6-12 \\\Leftrightarrow & -9x& = &-6 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-6}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{2}{3} & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-4x-6)& = & 3 \color{red}{-} (-14+x) \\\Leftrightarrow & -8x-12& = &3+14-x \\\Leftrightarrow & -8x \color{red}{-12} & = &17 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -8x+x& = &17+12 \\\Leftrightarrow & -7x& = &29 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{29}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-29}{7} & & \\ & V = \left\{ \frac{-29}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-5x-6)& = & 3 \color{red}{-} (8-4x) \\\Leftrightarrow & -25x-30& = &3-8+4x \\\Leftrightarrow & -25x \color{red}{-30} & = &-5 \color{red}{+4x} \\\Leftrightarrow & -25x \color{red}{-30} \color{blue}{+30} \color{blue}{-4x} & = &-5 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+30} \\\Leftrightarrow & -25x-4x& = &-5+30 \\\Leftrightarrow & -29x& = &25 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{25}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-25}{29} & & \\ & V = \left\{ \frac{-25}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-3x-1)& = & -15 \color{red}{-} (8-2x) \\\Leftrightarrow & -15x-5& = &-15-8+2x \\\Leftrightarrow & -15x \color{red}{-5} & = &-23 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-5} \color{blue}{+5} \color{blue}{-2x} & = &-23 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+5} \\\Leftrightarrow & -15x-2x& = &-23+5 \\\Leftrightarrow & -17x& = &-18 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-18}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{18}{17} & & \\ & V = \left\{ \frac{18}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-6x+3)& = & 9 \color{red}{-} (11+x) \\\Leftrightarrow & -18x+9& = &9-11-x \\\Leftrightarrow & -18x \color{red}{+9} & = &-2 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & -18x+x& = &-2-9 \\\Leftrightarrow & -17x& = &-11 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-11}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{11}{17} & & \\ & V = \left\{ \frac{11}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-6x+2)& = & -13 \color{red}{-} (-8+x) \\\Leftrightarrow & -24x+8& = &-13+8-x \\\Leftrightarrow & -24x \color{red}{+8} & = &-5 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -24x+x& = &-5-8 \\\Leftrightarrow & -23x& = &-13 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-13}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{13}{23} & & \\ & V = \left\{ \frac{13}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-4x+5)& = & 12 \color{red}{+} (1+x) \\\Leftrightarrow & -20x+25& = &12+1+x \\\Leftrightarrow & -20x \color{red}{+25} & = &13 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & -20x-x& = &13-25 \\\Leftrightarrow & -21x& = &-12 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-12}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{4}{7} & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-x-1)& = & 11 \color{red}{-} (2+x) \\\Leftrightarrow & -2x-2& = &11-2-x \\\Leftrightarrow & -2x \color{red}{-2} & = &9 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & -2x+x& = &9+2 \\\Leftrightarrow & -x& = &11 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{11}{ \color{red}{-1} } \\\Leftrightarrow & x = -11 & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (5x-4)& = & 4 \color{red}{-} (13+4x) \\\Leftrightarrow & 25x-20& = &4-13-4x \\\Leftrightarrow & 25x \color{red}{-20} & = &-9 \color{red}{-4x} \\\Leftrightarrow & 25x \color{red}{-20} \color{blue}{+20} \color{blue}{+4x} & = &-9 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+20} \\\Leftrightarrow & 25x+4x& = &-9+20 \\\Leftrightarrow & 29x& = &11 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{11}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{11}{29} & & \\ & V = \left\{ \frac{11}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (4x-3)& = & -10 \color{red}{+} (11+x) \\\Leftrightarrow & 12x-9& = &-10+11+x \\\Leftrightarrow & 12x \color{red}{-9} & = &1 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-9} \color{blue}{+9} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+9} \\\Leftrightarrow & 12x-x& = &1+9 \\\Leftrightarrow & 11x& = &10 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{10}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{10}{11} & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)