Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{5}{7})& = & -5x+\frac{7}{3} \\\Leftrightarrow & 12x-\frac{30}{7}& = & -5x+\frac{7}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x- \frac{90}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{49}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{-90} & = & \color{red}{-105x} +49 \\\Leftrightarrow & 252x \color{red}{-90} \color{blue}{+90} \color{blue}{+105x} & = & \color{red}{-105x} +49 \color{blue}{+105x} \color{blue}{+90} \\\Leftrightarrow & 252x+105x& = & 49+90 \\\Leftrightarrow & \color{red}{357} x& = & 139 \\\Leftrightarrow & x = \frac{139}{357} & & \\ & V = \left\{ \frac{139}{357} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{2}{3})& = & 4x+\frac{3}{7} \\\Leftrightarrow & -28x-\frac{14}{3}& = & 4x+\frac{3}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-588}{ \color{blue}{21} }x- \frac{98}{ \color{blue}{21} })& = & (\frac{84}{ \color{blue}{21} }x+ \frac{9}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -588x \color{red}{-98} & = & \color{red}{84x} +9 \\\Leftrightarrow & -588x \color{red}{-98} \color{blue}{+98} \color{blue}{-84x} & = & \color{red}{84x} +9 \color{blue}{-84x} \color{blue}{+98} \\\Leftrightarrow & -588x-84x& = & 9+98 \\\Leftrightarrow & \color{red}{-672} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-672} & & \\\Leftrightarrow & x = \frac{-107}{672} & & \\ & V = \left\{ \frac{-107}{672} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{5}{7})& = & -5x+\frac{10}{11} \\\Leftrightarrow & -24x+\frac{30}{7}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1848}{ \color{blue}{77} }x+ \frac{330}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1848x \color{red}{+330} & = & \color{red}{-385x} +70 \\\Leftrightarrow & -1848x \color{red}{+330} \color{blue}{-330} \color{blue}{+385x} & = & \color{red}{-385x} +70 \color{blue}{+385x} \color{blue}{-330} \\\Leftrightarrow & -1848x+385x& = & 70-330 \\\Leftrightarrow & \color{red}{-1463} x& = & -260 \\\Leftrightarrow & x = \frac{-260}{-1463} & & \\\Leftrightarrow & x = \frac{260}{1463} & & \\ & V = \left\{ \frac{260}{1463} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{5}{7})& = & 5x+\frac{3}{8} \\\Leftrightarrow & 12x+\frac{30}{7}& = & 5x+\frac{3}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{672}{ \color{blue}{56} }x+ \frac{240}{ \color{blue}{56} })& = & (\frac{280}{ \color{blue}{56} }x+ \frac{21}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 672x \color{red}{+240} & = & \color{red}{280x} +21 \\\Leftrightarrow & 672x \color{red}{+240} \color{blue}{-240} \color{blue}{-280x} & = & \color{red}{280x} +21 \color{blue}{-280x} \color{blue}{-240} \\\Leftrightarrow & 672x-280x& = & 21-240 \\\Leftrightarrow & \color{red}{392} x& = & -219 \\\Leftrightarrow & x = \frac{-219}{392} & & \\ & V = \left\{ \frac{-219}{392} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{4}{11})& = & 4x+\frac{3}{2} \\\Leftrightarrow & -28x-\frac{28}{11}& = & 4x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-616}{ \color{blue}{22} }x- \frac{56}{ \color{blue}{22} })& = & (\frac{88}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -616x \color{red}{-56} & = & \color{red}{88x} +33 \\\Leftrightarrow & -616x \color{red}{-56} \color{blue}{+56} \color{blue}{-88x} & = & \color{red}{88x} +33 \color{blue}{-88x} \color{blue}{+56} \\\Leftrightarrow & -616x-88x& = & 33+56 \\\Leftrightarrow & \color{red}{-704} x& = & 89 \\\Leftrightarrow & x = \frac{89}{-704} & & \\\Leftrightarrow & x = \frac{-89}{704} & & \\ & V = \left\{ \frac{-89}{704} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{3}{11})& = & -9x+\frac{2}{11} \\\Leftrightarrow & 16x+\frac{12}{11}& = & -9x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{176}{ \color{blue}{11} }x+ \frac{12}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 176x \color{red}{+12} & = & \color{red}{-99x} +2 \\\Leftrightarrow & 176x \color{red}{+12} \color{blue}{-12} \color{blue}{+99x} & = & \color{red}{-99x} +2 \color{blue}{+99x} \color{blue}{-12} \\\Leftrightarrow & 176x+99x& = & 2-12 \\\Leftrightarrow & \color{red}{275} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{275} & & \\\Leftrightarrow & x = \frac{-2}{55} & & \\ & V = \left\{ \frac{-2}{55} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{3}{7})& = & 9x+\frac{5}{2} \\\Leftrightarrow & -4x+\frac{6}{7}& = & 9x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-56}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{126}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -56x \color{red}{+12} & = & \color{red}{126x} +35 \\\Leftrightarrow & -56x \color{red}{+12} \color{blue}{-12} \color{blue}{-126x} & = & \color{red}{126x} +35 \color{blue}{-126x} \color{blue}{-12} \\\Leftrightarrow & -56x-126x& = & 35-12 \\\Leftrightarrow & \color{red}{-182} x& = & 23 \\\Leftrightarrow & x = \frac{23}{-182} & & \\\Leftrightarrow & x = \frac{-23}{182} & & \\ & V = \left\{ \frac{-23}{182} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{3}{7})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -6x+\frac{6}{7}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{+18} & = & \color{red}{147x} +14 \\\Leftrightarrow & -126x \color{red}{+18} \color{blue}{-18} \color{blue}{-147x} & = & \color{red}{147x} +14 \color{blue}{-147x} \color{blue}{-18} \\\Leftrightarrow & -126x-147x& = & 14-18 \\\Leftrightarrow & \color{red}{-273} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-273} & & \\\Leftrightarrow & x = \frac{4}{273} & & \\ & V = \left\{ \frac{4}{273} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{3}{7})& = & 8x+\frac{5}{7} \\\Leftrightarrow & 15x+\frac{9}{7}& = & 8x+\frac{5}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{105}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} })& = & (\frac{56}{ \color{blue}{7} }x+ \frac{5}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 105x \color{red}{+9} & = & \color{red}{56x} +5 \\\Leftrightarrow & 105x \color{red}{+9} \color{blue}{-9} \color{blue}{-56x} & = & \color{red}{56x} +5 \color{blue}{-56x} \color{blue}{-9} \\\Leftrightarrow & 105x-56x& = & 5-9 \\\Leftrightarrow & \color{red}{49} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{49} & & \\ & V = \left\{ \frac{-4}{49} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{3})& = & -2x+\frac{9}{2} \\\Leftrightarrow & 21x-\frac{14}{3}& = & -2x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{126}{ \color{blue}{6} }x- \frac{28}{ \color{blue}{6} })& = & (\frac{-12}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 126x \color{red}{-28} & = & \color{red}{-12x} +27 \\\Leftrightarrow & 126x \color{red}{-28} \color{blue}{+28} \color{blue}{+12x} & = & \color{red}{-12x} +27 \color{blue}{+12x} \color{blue}{+28} \\\Leftrightarrow & 126x+12x& = & 27+28 \\\Leftrightarrow & \color{red}{138} x& = & 55 \\\Leftrightarrow & x = \frac{55}{138} & & \\ & V = \left\{ \frac{55}{138} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{4}{5})& = & 5x+\frac{3}{7} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+84} & = & \color{red}{175x} +15 \\\Leftrightarrow & -420x \color{red}{+84} \color{blue}{-84} \color{blue}{-175x} & = & \color{red}{175x} +15 \color{blue}{-175x} \color{blue}{-84} \\\Leftrightarrow & -420x-175x& = & 15-84 \\\Leftrightarrow & \color{red}{-595} x& = & -69 \\\Leftrightarrow & x = \frac{-69}{-595} & & \\\Leftrightarrow & x = \frac{69}{595} & & \\ & V = \left\{ \frac{69}{595} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{4}{3})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 28x+\frac{28}{3}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{924}{ \color{blue}{33} }x+ \frac{308}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 924x \color{red}{+308} & = & \color{red}{165x} +18 \\\Leftrightarrow & 924x \color{red}{+308} \color{blue}{-308} \color{blue}{-165x} & = & \color{red}{165x} +18 \color{blue}{-165x} \color{blue}{-308} \\\Leftrightarrow & 924x-165x& = & 18-308 \\\Leftrightarrow & \color{red}{759} x& = & -290 \\\Leftrightarrow & x = \frac{-290}{759} & & \\ & V = \left\{ \frac{-290}{759} \right\} & \\\end{align}\)