Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-x+3)& = & 15 \color{red}{+} (-4+x) \\\Leftrightarrow & -2x+6& = &15-4+x \\\Leftrightarrow & -2x \color{red}{+6} & = &11 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -2x-x& = &11-6 \\\Leftrightarrow & -3x& = &5 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{5}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-5}{3} & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (2x-4)& = & 9 \color{red}{+} (-12+3x) \\\Leftrightarrow & 8x-16& = &9-12+3x \\\Leftrightarrow & 8x \color{red}{-16} & = &-3 \color{red}{+3x} \\\Leftrightarrow & 8x \color{red}{-16} \color{blue}{+16} \color{blue}{-3x} & = &-3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+16} \\\Leftrightarrow & 8x-3x& = &-3+16 \\\Leftrightarrow & 5x& = &13 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{13}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{13}{5} & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-5x+3)& = & 3 \color{red}{-} (14+x) \\\Leftrightarrow & -25x+15& = &3-14-x \\\Leftrightarrow & -25x \color{red}{+15} & = &-11 \color{red}{-x} \\\Leftrightarrow & -25x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -25x+x& = &-11-15 \\\Leftrightarrow & -24x& = &-26 \\\Leftrightarrow & \frac{-24x}{ \color{red}{-24} }& = &\frac{-26}{ \color{red}{-24} } \\\Leftrightarrow & x = \frac{13}{12} & & \\ & V = \left\{ \frac{13}{12} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-4x-4)& = & 4 \color{red}{+} (15+x) \\\Leftrightarrow & -12x-12& = &4+15+x \\\Leftrightarrow & -12x \color{red}{-12} & = &19 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -12x-x& = &19+12 \\\Leftrightarrow & -13x& = &31 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{31}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-31}{13} & & \\ & V = \left\{ \frac{-31}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-4x-3)& = & 10 \color{red}{+} (15-5x) \\\Leftrightarrow & -8x-6& = &10+15-5x \\\Leftrightarrow & -8x \color{red}{-6} & = &25 \color{red}{-5x} \\\Leftrightarrow & -8x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &25 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & -8x+5x& = &25+6 \\\Leftrightarrow & -3x& = &31 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{31}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-31}{3} & & \\ & V = \left\{ \frac{-31}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (2x-3)& = & -1 \color{red}{+} (8+3x) \\\Leftrightarrow & 10x-15& = &-1+8+3x \\\Leftrightarrow & 10x \color{red}{-15} & = &7 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-15} \color{blue}{+15} \color{blue}{-3x} & = &7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+15} \\\Leftrightarrow & 10x-3x& = &7+15 \\\Leftrightarrow & 7x& = &22 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{22}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{22}{7} & & \\ & V = \left\{ \frac{22}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (x-4)& = & -10 \color{red}{+} (12+x) \\\Leftrightarrow & 4x-16& = &-10+12+x \\\Leftrightarrow & 4x \color{red}{-16} & = &2 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & 4x-x& = &2+16 \\\Leftrightarrow & 3x& = &18 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{18}{ \color{red}{3} } \\\Leftrightarrow & x = 6 & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-3x-3)& = & 4 \color{red}{-} (5-4x) \\\Leftrightarrow & -9x-9& = &4-5+4x \\\Leftrightarrow & -9x \color{red}{-9} & = &-1 \color{red}{+4x} \\\Leftrightarrow & -9x \color{red}{-9} \color{blue}{+9} \color{blue}{-4x} & = &-1 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+9} \\\Leftrightarrow & -9x-4x& = &-1+9 \\\Leftrightarrow & -13x& = &8 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{8}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (x+4)& = & 13 \color{red}{+} (-10-4x) \\\Leftrightarrow & 5x+20& = &13-10-4x \\\Leftrightarrow & 5x \color{red}{+20} & = &3 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{+20} \color{blue}{-20} \color{blue}{+4x} & = &3 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-20} \\\Leftrightarrow & 5x+4x& = &3-20 \\\Leftrightarrow & 9x& = &-17 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-17}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-17}{9} & & \\ & V = \left\{ \frac{-17}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (4x-5)& = & -8 \color{red}{-} (-3+x) \\\Leftrightarrow & 12x-15& = &-8+3-x \\\Leftrightarrow & 12x \color{red}{-15} & = &-5 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 12x+x& = &-5+15 \\\Leftrightarrow & 13x& = &10 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{10}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{10}{13} & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (x+1)& = & 2 \color{red}{+} (13+x) \\\Leftrightarrow & 3x+3& = &2+13+x \\\Leftrightarrow & 3x \color{red}{+3} & = &15 \color{red}{+x} \\\Leftrightarrow & 3x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & 3x-x& = &15-3 \\\Leftrightarrow & 2x& = &12 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{12}{ \color{red}{2} } \\\Leftrightarrow & x = 6 & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (5x+1)& = & -9 \color{red}{-} (-1+4x) \\\Leftrightarrow & 15x+3& = &-9+1-4x \\\Leftrightarrow & 15x \color{red}{+3} & = &-8 \color{red}{-4x} \\\Leftrightarrow & 15x \color{red}{+3} \color{blue}{-3} \color{blue}{+4x} & = &-8 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-3} \\\Leftrightarrow & 15x+4x& = &-8-3 \\\Leftrightarrow & 19x& = &-11 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-11}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-11}{19} & & \\ & V = \left\{ \frac{-11}{19} \right\} & \\\end{align}\)