Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{5}{7})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -12x-\frac{30}{7}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x- \frac{90}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{-90} & = & \color{red}{105x} +56 \\\Leftrightarrow & -252x \color{red}{-90} \color{blue}{+90} \color{blue}{-105x} & = & \color{red}{105x} +56 \color{blue}{-105x} \color{blue}{+90} \\\Leftrightarrow & -252x-105x& = & 56+90 \\\Leftrightarrow & \color{red}{-357} x& = & 146 \\\Leftrightarrow & x = \frac{146}{-357} & & \\\Leftrightarrow & x = \frac{-146}{357} & & \\ & V = \left\{ \frac{-146}{357} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{3}{11})& = & -5x+\frac{7}{6} \\\Leftrightarrow & -24x-\frac{18}{11}& = & -5x+\frac{7}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-1584}{ \color{blue}{66} }x- \frac{108}{ \color{blue}{66} })& = & (\frac{-330}{ \color{blue}{66} }x+ \frac{77}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -1584x \color{red}{-108} & = & \color{red}{-330x} +77 \\\Leftrightarrow & -1584x \color{red}{-108} \color{blue}{+108} \color{blue}{+330x} & = & \color{red}{-330x} +77 \color{blue}{+330x} \color{blue}{+108} \\\Leftrightarrow & -1584x+330x& = & 77+108 \\\Leftrightarrow & \color{red}{-1254} x& = & 185 \\\Leftrightarrow & x = \frac{185}{-1254} & & \\\Leftrightarrow & x = \frac{-185}{1254} & & \\ & V = \left\{ \frac{-185}{1254} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{3}{2})& = & 7x+\frac{2}{9} \\\Leftrightarrow & 12x+\frac{9}{2}& = & 7x+\frac{2}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{216}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} })& = & (\frac{126}{ \color{blue}{18} }x+ \frac{4}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 216x \color{red}{+81} & = & \color{red}{126x} +4 \\\Leftrightarrow & 216x \color{red}{+81} \color{blue}{-81} \color{blue}{-126x} & = & \color{red}{126x} +4 \color{blue}{-126x} \color{blue}{-81} \\\Leftrightarrow & 216x-126x& = & 4-81 \\\Leftrightarrow & \color{red}{90} x& = & -77 \\\Leftrightarrow & x = \frac{-77}{90} & & \\ & V = \left\{ \frac{-77}{90} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{3}{5})& = & -9x+\frac{3}{5} \\\Leftrightarrow & -8x+\frac{12}{5}& = & -9x+\frac{3}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-40}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-45}{ \color{blue}{5} }x+ \frac{3}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -40x \color{red}{+12} & = & \color{red}{-45x} +3 \\\Leftrightarrow & -40x \color{red}{+12} \color{blue}{-12} \color{blue}{+45x} & = & \color{red}{-45x} +3 \color{blue}{+45x} \color{blue}{-12} \\\Leftrightarrow & -40x+45x& = & 3-12 \\\Leftrightarrow & \color{red}{5} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{5} & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{2}{3})& = & 3x+\frac{9}{8} \\\Leftrightarrow & 8x+\frac{8}{3}& = & 3x+\frac{9}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{192}{ \color{blue}{24} }x+ \frac{64}{ \color{blue}{24} })& = & (\frac{72}{ \color{blue}{24} }x+ \frac{27}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 192x \color{red}{+64} & = & \color{red}{72x} +27 \\\Leftrightarrow & 192x \color{red}{+64} \color{blue}{-64} \color{blue}{-72x} & = & \color{red}{72x} +27 \color{blue}{-72x} \color{blue}{-64} \\\Leftrightarrow & 192x-72x& = & 27-64 \\\Leftrightarrow & \color{red}{120} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{120} & & \\ & V = \left\{ \frac{-37}{120} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{5}{3})& = & -7x+\frac{4}{11} \\\Leftrightarrow & 10x+\frac{10}{3}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{330}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 330x \color{red}{+110} & = & \color{red}{-231x} +12 \\\Leftrightarrow & 330x \color{red}{+110} \color{blue}{-110} \color{blue}{+231x} & = & \color{red}{-231x} +12 \color{blue}{+231x} \color{blue}{-110} \\\Leftrightarrow & 330x+231x& = & 12-110 \\\Leftrightarrow & \color{red}{561} x& = & -98 \\\Leftrightarrow & x = \frac{-98}{561} & & \\ & V = \left\{ \frac{-98}{561} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{4}{9})& = & 5x+\frac{2}{5} \\\Leftrightarrow & 6x-\frac{8}{9}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{270}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{18}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 270x \color{red}{-40} & = & \color{red}{225x} +18 \\\Leftrightarrow & 270x \color{red}{-40} \color{blue}{+40} \color{blue}{-225x} & = & \color{red}{225x} +18 \color{blue}{-225x} \color{blue}{+40} \\\Leftrightarrow & 270x-225x& = & 18+40 \\\Leftrightarrow & \color{red}{45} x& = & 58 \\\Leftrightarrow & x = \frac{58}{45} & & \\ & V = \left\{ \frac{58}{45} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{3}{5})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -16x-\frac{12}{5}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-240}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -240x \color{red}{-36} & = & \color{red}{105x} +10 \\\Leftrightarrow & -240x \color{red}{-36} \color{blue}{+36} \color{blue}{-105x} & = & \color{red}{105x} +10 \color{blue}{-105x} \color{blue}{+36} \\\Leftrightarrow & -240x-105x& = & 10+36 \\\Leftrightarrow & \color{red}{-345} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-345} & & \\\Leftrightarrow & x = \frac{-2}{15} & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{2}{9})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 12x-\frac{8}{9}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{540}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 540x \color{red}{-40} & = & \color{red}{-315x} +54 \\\Leftrightarrow & 540x \color{red}{-40} \color{blue}{+40} \color{blue}{+315x} & = & \color{red}{-315x} +54 \color{blue}{+315x} \color{blue}{+40} \\\Leftrightarrow & 540x+315x& = & 54+40 \\\Leftrightarrow & \color{red}{855} x& = & 94 \\\Leftrightarrow & x = \frac{94}{855} & & \\ & V = \left\{ \frac{94}{855} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{2}{7})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -6x+\frac{4}{7}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{+12} & = & \color{red}{147x} +14 \\\Leftrightarrow & -126x \color{red}{+12} \color{blue}{-12} \color{blue}{-147x} & = & \color{red}{147x} +14 \color{blue}{-147x} \color{blue}{-12} \\\Leftrightarrow & -126x-147x& = & 14-12 \\\Leftrightarrow & \color{red}{-273} x& = & 2 \\\Leftrightarrow & x = \frac{2}{-273} & & \\\Leftrightarrow & x = \frac{-2}{273} & & \\ & V = \left\{ \frac{-2}{273} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{5}{8})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 12x-\frac{15}{8}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{672}{ \color{blue}{56} }x- \frac{105}{ \color{blue}{56} })& = & (\frac{280}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 672x \color{red}{-105} & = & \color{red}{280x} +80 \\\Leftrightarrow & 672x \color{red}{-105} \color{blue}{+105} \color{blue}{-280x} & = & \color{red}{280x} +80 \color{blue}{-280x} \color{blue}{+105} \\\Leftrightarrow & 672x-280x& = & 80+105 \\\Leftrightarrow & \color{red}{392} x& = & 185 \\\Leftrightarrow & x = \frac{185}{392} & & \\ & V = \left\{ \frac{185}{392} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{5}{7})& = & 5x+\frac{8}{9} \\\Leftrightarrow & -24x-\frac{30}{7}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1512}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1512x \color{red}{-270} & = & \color{red}{315x} +56 \\\Leftrightarrow & -1512x \color{red}{-270} \color{blue}{+270} \color{blue}{-315x} & = & \color{red}{315x} +56 \color{blue}{-315x} \color{blue}{+270} \\\Leftrightarrow & -1512x-315x& = & 56+270 \\\Leftrightarrow & \color{red}{-1827} x& = & 326 \\\Leftrightarrow & x = \frac{326}{-1827} & & \\\Leftrightarrow & x = \frac{-326}{1827} & & \\ & V = \left\{ \frac{-326}{1827} \right\} & \\\end{align}\)