Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{3}{2})& = & -5x+\frac{8}{7} \\\Leftrightarrow & 12x+\frac{9}{2}& = & -5x+\frac{8}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{168}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{16}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 168x \color{red}{+63} & = & \color{red}{-70x} +16 \\\Leftrightarrow & 168x \color{red}{+63} \color{blue}{-63} \color{blue}{+70x} & = & \color{red}{-70x} +16 \color{blue}{+70x} \color{blue}{-63} \\\Leftrightarrow & 168x+70x& = & 16-63 \\\Leftrightarrow & \color{red}{238} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{238} & & \\ & V = \left\{ \frac{-47}{238} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{3}{8})& = & -4x+\frac{6}{11} \\\Leftrightarrow & 21x+\frac{21}{8}& = & -4x+\frac{6}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1848}{ \color{blue}{88} }x+ \frac{231}{ \color{blue}{88} })& = & (\frac{-352}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1848x \color{red}{+231} & = & \color{red}{-352x} +48 \\\Leftrightarrow & 1848x \color{red}{+231} \color{blue}{-231} \color{blue}{+352x} & = & \color{red}{-352x} +48 \color{blue}{+352x} \color{blue}{-231} \\\Leftrightarrow & 1848x+352x& = & 48-231 \\\Leftrightarrow & \color{red}{2200} x& = & -183 \\\Leftrightarrow & x = \frac{-183}{2200} & & \\ & V = \left\{ \frac{-183}{2200} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{8})& = & -7x+\frac{9}{4} \\\Leftrightarrow & -28x+\frac{21}{8}& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-224}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{-56}{ \color{blue}{8} }x+ \frac{18}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -224x \color{red}{+21} & = & \color{red}{-56x} +18 \\\Leftrightarrow & -224x \color{red}{+21} \color{blue}{-21} \color{blue}{+56x} & = & \color{red}{-56x} +18 \color{blue}{+56x} \color{blue}{-21} \\\Leftrightarrow & -224x+56x& = & 18-21 \\\Leftrightarrow & \color{red}{-168} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-168} & & \\\Leftrightarrow & x = \frac{1}{56} & & \\ & V = \left\{ \frac{1}{56} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{2}{3})& = & -7x+\frac{5}{11} \\\Leftrightarrow & -20x-\frac{10}{3}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x- \frac{110}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{-110} & = & \color{red}{-231x} +15 \\\Leftrightarrow & -660x \color{red}{-110} \color{blue}{+110} \color{blue}{+231x} & = & \color{red}{-231x} +15 \color{blue}{+231x} \color{blue}{+110} \\\Leftrightarrow & -660x+231x& = & 15+110 \\\Leftrightarrow & \color{red}{-429} x& = & 125 \\\Leftrightarrow & x = \frac{125}{-429} & & \\\Leftrightarrow & x = \frac{-125}{429} & & \\ & V = \left\{ \frac{-125}{429} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{2}{5})& = & -3x+\frac{4}{5} \\\Leftrightarrow & -18x+\frac{12}{5}& = & -3x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-90}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-15}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -90x \color{red}{+12} & = & \color{red}{-15x} +4 \\\Leftrightarrow & -90x \color{red}{+12} \color{blue}{-12} \color{blue}{+15x} & = & \color{red}{-15x} +4 \color{blue}{+15x} \color{blue}{-12} \\\Leftrightarrow & -90x+15x& = & 4-12 \\\Leftrightarrow & \color{red}{-75} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-75} & & \\\Leftrightarrow & x = \frac{8}{75} & & \\ & V = \left\{ \frac{8}{75} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{3}{11})& = & 5x+\frac{2}{3} \\\Leftrightarrow & -12x-\frac{12}{11}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x- \frac{36}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{-36} & = & \color{red}{165x} +22 \\\Leftrightarrow & -396x \color{red}{-36} \color{blue}{+36} \color{blue}{-165x} & = & \color{red}{165x} +22 \color{blue}{-165x} \color{blue}{+36} \\\Leftrightarrow & -396x-165x& = & 22+36 \\\Leftrightarrow & \color{red}{-561} x& = & 58 \\\Leftrightarrow & x = \frac{58}{-561} & & \\\Leftrightarrow & x = \frac{-58}{561} & & \\ & V = \left\{ \frac{-58}{561} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{5}{11})& = & 9x+\frac{6}{5} \\\Leftrightarrow & 4x+\frac{10}{11}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{220}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 220x \color{red}{+50} & = & \color{red}{495x} +66 \\\Leftrightarrow & 220x \color{red}{+50} \color{blue}{-50} \color{blue}{-495x} & = & \color{red}{495x} +66 \color{blue}{-495x} \color{blue}{-50} \\\Leftrightarrow & 220x-495x& = & 66-50 \\\Leftrightarrow & \color{red}{-275} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-275} & & \\\Leftrightarrow & x = \frac{-16}{275} & & \\ & V = \left\{ \frac{-16}{275} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{2}{7})& = & 3x+\frac{6}{7} \\\Leftrightarrow & 25x-\frac{10}{7}& = & 3x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{175}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{21}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 175x \color{red}{-10} & = & \color{red}{21x} +6 \\\Leftrightarrow & 175x \color{red}{-10} \color{blue}{+10} \color{blue}{-21x} & = & \color{red}{21x} +6 \color{blue}{-21x} \color{blue}{+10} \\\Leftrightarrow & 175x-21x& = & 6+10 \\\Leftrightarrow & \color{red}{154} x& = & 16 \\\Leftrightarrow & x = \frac{16}{154} & & \\\Leftrightarrow & x = \frac{8}{77} & & \\ & V = \left\{ \frac{8}{77} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{4}{11})& = & -6x+\frac{8}{3} \\\Leftrightarrow & -25x+\frac{20}{11}& = & -6x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-825}{ \color{blue}{33} }x+ \frac{60}{ \color{blue}{33} })& = & (\frac{-198}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -825x \color{red}{+60} & = & \color{red}{-198x} +88 \\\Leftrightarrow & -825x \color{red}{+60} \color{blue}{-60} \color{blue}{+198x} & = & \color{red}{-198x} +88 \color{blue}{+198x} \color{blue}{-60} \\\Leftrightarrow & -825x+198x& = & 88-60 \\\Leftrightarrow & \color{red}{-627} x& = & 28 \\\Leftrightarrow & x = \frac{28}{-627} & & \\\Leftrightarrow & x = \frac{-28}{627} & & \\ & V = \left\{ \frac{-28}{627} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{4}{5})& = & 7x+\frac{4}{9} \\\Leftrightarrow & -24x-\frac{24}{5}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1080}{ \color{blue}{45} }x- \frac{216}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1080x \color{red}{-216} & = & \color{red}{315x} +20 \\\Leftrightarrow & -1080x \color{red}{-216} \color{blue}{+216} \color{blue}{-315x} & = & \color{red}{315x} +20 \color{blue}{-315x} \color{blue}{+216} \\\Leftrightarrow & -1080x-315x& = & 20+216 \\\Leftrightarrow & \color{red}{-1395} x& = & 236 \\\Leftrightarrow & x = \frac{236}{-1395} & & \\\Leftrightarrow & x = \frac{-236}{1395} & & \\ & V = \left\{ \frac{-236}{1395} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{5}{7})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 30x-\frac{30}{7}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{420}{ \color{blue}{14} }x- \frac{60}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 420x \color{red}{-60} & = & \color{red}{-98x} +21 \\\Leftrightarrow & 420x \color{red}{-60} \color{blue}{+60} \color{blue}{+98x} & = & \color{red}{-98x} +21 \color{blue}{+98x} \color{blue}{+60} \\\Leftrightarrow & 420x+98x& = & 21+60 \\\Leftrightarrow & \color{red}{518} x& = & 81 \\\Leftrightarrow & x = \frac{81}{518} & & \\ & V = \left\{ \frac{81}{518} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{3}{11})& = & -2x+\frac{4}{11} \\\Leftrightarrow & -18x-\frac{18}{11}& = & -2x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-198}{ \color{blue}{11} }x- \frac{18}{ \color{blue}{11} })& = & (\frac{-22}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -198x \color{red}{-18} & = & \color{red}{-22x} +4 \\\Leftrightarrow & -198x \color{red}{-18} \color{blue}{+18} \color{blue}{+22x} & = & \color{red}{-22x} +4 \color{blue}{+22x} \color{blue}{+18} \\\Leftrightarrow & -198x+22x& = & 4+18 \\\Leftrightarrow & \color{red}{-176} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-176} & & \\\Leftrightarrow & x = \frac{-1}{8} & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)