Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{3}{4})& = & 3x+\frac{4}{7} \\\Leftrightarrow & -14x-\frac{21}{4}& = & 3x+\frac{4}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-392}{ \color{blue}{28} }x- \frac{147}{ \color{blue}{28} })& = & (\frac{84}{ \color{blue}{28} }x+ \frac{16}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -392x \color{red}{-147} & = & \color{red}{84x} +16 \\\Leftrightarrow & -392x \color{red}{-147} \color{blue}{+147} \color{blue}{-84x} & = & \color{red}{84x} +16 \color{blue}{-84x} \color{blue}{+147} \\\Leftrightarrow & -392x-84x& = & 16+147 \\\Leftrightarrow & \color{red}{-476} x& = & 163 \\\Leftrightarrow & x = \frac{163}{-476} & & \\\Leftrightarrow & x = \frac{-163}{476} & & \\ & V = \left\{ \frac{-163}{476} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{2}{3})& = & 3x+\frac{2}{3} \\\Leftrightarrow & 10x+\frac{4}{3}& = & 3x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{30}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 30x \color{red}{+4} & = & \color{red}{9x} +2 \\\Leftrightarrow & 30x \color{red}{+4} \color{blue}{-4} \color{blue}{-9x} & = & \color{red}{9x} +2 \color{blue}{-9x} \color{blue}{-4} \\\Leftrightarrow & 30x-9x& = & 2-4 \\\Leftrightarrow & \color{red}{21} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{21} & & \\ & V = \left\{ \frac{-2}{21} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{4}{3})& = & 5x+\frac{8}{5} \\\Leftrightarrow & -12x+\frac{16}{3}& = & 5x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x+ \frac{80}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{+80} & = & \color{red}{75x} +24 \\\Leftrightarrow & -180x \color{red}{+80} \color{blue}{-80} \color{blue}{-75x} & = & \color{red}{75x} +24 \color{blue}{-75x} \color{blue}{-80} \\\Leftrightarrow & -180x-75x& = & 24-80 \\\Leftrightarrow & \color{red}{-255} x& = & -56 \\\Leftrightarrow & x = \frac{-56}{-255} & & \\\Leftrightarrow & x = \frac{56}{255} & & \\ & V = \left\{ \frac{56}{255} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{5}{11})& = & 7x+\frac{8}{9} \\\Leftrightarrow & 10x-\frac{25}{11}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{990}{ \color{blue}{99} }x- \frac{225}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 990x \color{red}{-225} & = & \color{red}{693x} +88 \\\Leftrightarrow & 990x \color{red}{-225} \color{blue}{+225} \color{blue}{-693x} & = & \color{red}{693x} +88 \color{blue}{-693x} \color{blue}{+225} \\\Leftrightarrow & 990x-693x& = & 88+225 \\\Leftrightarrow & \color{red}{297} x& = & 313 \\\Leftrightarrow & x = \frac{313}{297} & & \\ & V = \left\{ \frac{313}{297} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{2}{9})& = & 5x+\frac{7}{11} \\\Leftrightarrow & -12x+\frac{8}{9}& = & 5x+\frac{7}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1188}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{63}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1188x \color{red}{+88} & = & \color{red}{495x} +63 \\\Leftrightarrow & -1188x \color{red}{+88} \color{blue}{-88} \color{blue}{-495x} & = & \color{red}{495x} +63 \color{blue}{-495x} \color{blue}{-88} \\\Leftrightarrow & -1188x-495x& = & 63-88 \\\Leftrightarrow & \color{red}{-1683} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{-1683} & & \\\Leftrightarrow & x = \frac{25}{1683} & & \\ & V = \left\{ \frac{25}{1683} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{3}{11})& = & 3x+\frac{5}{12} \\\Leftrightarrow & 10x-\frac{15}{11}& = & 3x+\frac{5}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{1320}{ \color{blue}{132} }x- \frac{180}{ \color{blue}{132} })& = & (\frac{396}{ \color{blue}{132} }x+ \frac{55}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & 1320x \color{red}{-180} & = & \color{red}{396x} +55 \\\Leftrightarrow & 1320x \color{red}{-180} \color{blue}{+180} \color{blue}{-396x} & = & \color{red}{396x} +55 \color{blue}{-396x} \color{blue}{+180} \\\Leftrightarrow & 1320x-396x& = & 55+180 \\\Leftrightarrow & \color{red}{924} x& = & 235 \\\Leftrightarrow & x = \frac{235}{924} & & \\ & V = \left\{ \frac{235}{924} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{4}{9})& = & 9x+\frac{4}{9} \\\Leftrightarrow & 28x-\frac{28}{9}& = & 9x+\frac{4}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{252}{ \color{blue}{9} }x- \frac{28}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 252x \color{red}{-28} & = & \color{red}{81x} +4 \\\Leftrightarrow & 252x \color{red}{-28} \color{blue}{+28} \color{blue}{-81x} & = & \color{red}{81x} +4 \color{blue}{-81x} \color{blue}{+28} \\\Leftrightarrow & 252x-81x& = & 4+28 \\\Leftrightarrow & \color{red}{171} x& = & 32 \\\Leftrightarrow & x = \frac{32}{171} & & \\ & V = \left\{ \frac{32}{171} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{1}{2})& = & -9x+\frac{4}{9} \\\Leftrightarrow & 35x-\frac{7}{2}& = & -9x+\frac{4}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{630}{ \color{blue}{18} }x- \frac{63}{ \color{blue}{18} })& = & (\frac{-162}{ \color{blue}{18} }x+ \frac{8}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 630x \color{red}{-63} & = & \color{red}{-162x} +8 \\\Leftrightarrow & 630x \color{red}{-63} \color{blue}{+63} \color{blue}{+162x} & = & \color{red}{-162x} +8 \color{blue}{+162x} \color{blue}{+63} \\\Leftrightarrow & 630x+162x& = & 8+63 \\\Leftrightarrow & \color{red}{792} x& = & 71 \\\Leftrightarrow & x = \frac{71}{792} & & \\ & V = \left\{ \frac{71}{792} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{3}{11})& = & -7x+\frac{4}{11} \\\Leftrightarrow & 30x-\frac{18}{11}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{330}{ \color{blue}{11} }x- \frac{18}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 330x \color{red}{-18} & = & \color{red}{-77x} +4 \\\Leftrightarrow & 330x \color{red}{-18} \color{blue}{+18} \color{blue}{+77x} & = & \color{red}{-77x} +4 \color{blue}{+77x} \color{blue}{+18} \\\Leftrightarrow & 330x+77x& = & 4+18 \\\Leftrightarrow & \color{red}{407} x& = & 22 \\\Leftrightarrow & x = \frac{22}{407} & & \\\Leftrightarrow & x = \frac{2}{37} & & \\ & V = \left\{ \frac{2}{37} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{4}{11})& = & 5x+\frac{4}{5} \\\Leftrightarrow & 8x-\frac{16}{11}& = & 5x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x- \frac{80}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{-80} & = & \color{red}{275x} +44 \\\Leftrightarrow & 440x \color{red}{-80} \color{blue}{+80} \color{blue}{-275x} & = & \color{red}{275x} +44 \color{blue}{-275x} \color{blue}{+80} \\\Leftrightarrow & 440x-275x& = & 44+80 \\\Leftrightarrow & \color{red}{165} x& = & 124 \\\Leftrightarrow & x = \frac{124}{165} & & \\ & V = \left\{ \frac{124}{165} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{5}{2})& = & -4x+\frac{10}{11} \\\Leftrightarrow & 15x-\frac{15}{2}& = & -4x+\frac{10}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{330}{ \color{blue}{22} }x- \frac{165}{ \color{blue}{22} })& = & (\frac{-88}{ \color{blue}{22} }x+ \frac{20}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 330x \color{red}{-165} & = & \color{red}{-88x} +20 \\\Leftrightarrow & 330x \color{red}{-165} \color{blue}{+165} \color{blue}{+88x} & = & \color{red}{-88x} +20 \color{blue}{+88x} \color{blue}{+165} \\\Leftrightarrow & 330x+88x& = & 20+165 \\\Leftrightarrow & \color{red}{418} x& = & 185 \\\Leftrightarrow & x = \frac{185}{418} & & \\ & V = \left\{ \frac{185}{418} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{5}{9})& = & -7x+\frac{3}{7} \\\Leftrightarrow & -10x-\frac{10}{9}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-630}{ \color{blue}{63} }x- \frac{70}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{27}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -630x \color{red}{-70} & = & \color{red}{-441x} +27 \\\Leftrightarrow & -630x \color{red}{-70} \color{blue}{+70} \color{blue}{+441x} & = & \color{red}{-441x} +27 \color{blue}{+441x} \color{blue}{+70} \\\Leftrightarrow & -630x+441x& = & 27+70 \\\Leftrightarrow & \color{red}{-189} x& = & 97 \\\Leftrightarrow & x = \frac{97}{-189} & & \\\Leftrightarrow & x = \frac{-97}{189} & & \\ & V = \left\{ \frac{-97}{189} \right\} & \\\end{align}\)